I would use the mastic for sure and leave the tape alone. I am not sure of the best way to deal with the insulation as mine still has none yet. I will from experience on sealing my system tell you that every hour spent will pay off on the utility bills and comfort level. I just had 2x4s blocking the return cavities in my walls that of which some had over 1/2" of space allowing air to be pulled from my attic and even worse sealing where the return trunk met the return bays in the floor joists. I was pulling air from the basement and attic as much as the interior of the home itself. I had major leaks at the trunk to duct connections that I previously taped but the tape came loose. I attacked everything with mastic and chip brushes along with a few cans of foam and fireblock foam. I believe I used 3 gallons of mastic to seal mine up. I also swiped the rotation joints of all 90's and trunk seams.
On the cautionary side if you do not have enough return area (enough return vents and no restricted areas in the duct runs) and you seal everything up tight, it could overheat the blower motor.

For example on my home I had 2-6x30" return vents and 2-6x14" return vents in 2z4 walls and only had 3x6" holes cut through the floor to the basement where the returns ran to the trunk. so I had 6-3x6" holes for air to flow through back to the furnace. I opened them up to 3x12-14 and added one additional 6x30 vent in a hall before I sealed anything. I had 108sq in of open return flow area and opened it up to over 288sq in. I also made one of the openings 6x14 by using up some closet space in one room that was always cooler/warmer than the rest of the house to pull more air from that room.
I fixed the room that was always a minimum of 6 degrees warmer or colder than the rest of the house and brought it to within 2 degrees of the thermostat. The return air temp at the furnace is almost identical to the temp in the home when it used to be +5 or more in the summer and -5 or more in the winter. I achieved all of this so far with NO DUCT INSULATION!! I plan to add duct insulation just will attack that come winter. I know this is a long post but I am trying to show how important and what a difference having things sealed up and things set up right can make!

Sadly the time I spent so far was well more than 40 hours total working a few here and a few there... but if it was done at the time of installation and or home building it could have all been done in an extra 8 hour day easily.

vanenk.
so you have hard duct insulated with duct wrap.
you can open the ductwrap, do the work and reuse the
ductwrap once mastic has dried.
to reinstall the wrap
you can staple with duct stapl gun..the difference a duct wrap staple gun and a regular staple gun is that the staple
spreads out instead of in, giving you holding area for the duct wrap.
once duct wrap is stapled in place you seal it with duct wrap tape..looks like ductwrap..shiny with nylon scrim. this is placed over the stapled seam of the duct wrap. surfaces must be dry and clean for tape to adhere.

for me..tester of ductwork,and sometimes sealer of ductwork
these are the areas I address first.

1-supply plenum to air handler unit/furnace..I generally use
Hardcast mastic tape for this...
2-then the return air connection to the air handler unit..
again mastic tape.
3-duct takeoffs at the plenum.
pull the ductwrap back and take a look at where it exits the plenum. if the unit is running you will feel the air leakage. Mastic..the paint on type works best. remove ductwrap..gently as you want to reuse..and fold it back to where you have access to the start collar/takeoff. use a 2" cheap paint brush and mastic seal..access and seal several ducts at a time..give it time for the mastic to set up before reattaching duct wrap.

4-if the ducts have 90's seal the joints in the 90's both at plenum and supply boxes. Wye boxes (also called junction boxes, Y's... should also be sealed.

this is where I would stop, and move on to supply boxes and return air.

while there is a lateral seam where all runs of hard pipe are joined..this would encompass un-insulating, sealing and re-insulation. an hvac company would charge you a fortune for this..as would I..its a big big job.

I would concentrate onreturn and supply to unit, then plenum to ducts ...junctions and finally supply boxes. My testing shows that duct leakage on hard pipe comes mostly from the areas listed above.

5-to seal the supply boxes I have found that it is easier to
access them by removing the register inside the house and sealing the gap between the supply box and the sheetrock with mastic tape.

6-return air should also be sealed, if it is dirty this is an indication of air leakage. if you have a ceiling return you should caulk all the joints between the 2x's. this can be done from both attic and interior.
7-return air chases are more complicated to seal.

Hardcast mastic tape, and paint on mastics (Irongrip etc)
are available at hvac supply stores. you may find mastic at
box stores, but the tape..which is fast and easy to install is not sold there, cheap knockoffs that will fail..but not a good long lasting mastic tape.
been there..seen that!

hope this will be a start for you.
the state and federal programs I work with mandate
5% duct loss..it can be done, but its difficult in existing
homes. with hard pipe if you can achieve 5%..I may be calling you!!

look for dirt on the ductwrap. these dirty areas are indications of duct leakage.
best of luck.

Country and energy,

Thanks for the great insight! Again, knowing what needs to be done versus how best to do it is what makes the difference. I've had the return sealed up with mastic/caulk/foam board, and have adequate return area (2 sq ft per ton).

I know it's gonna take time, that's OK, I just want to maximize my efforts, and you guys have shown me exactly how to do that!

Props to both of you! You've been great help!

Many thanks to ENERGY_RATER_LA for the excellent information!

Be careful working in your attics.
Make sure you have plenty of light.
I use 1x12x6 walkboards to safely reach all
areas, and put my stuff in a sturdy plastic crate
to move from area to area.
if you have return air chases..I can walk you
through sealing of them if needed.
you are both welcome. and as always...
best of luck!

Energy,

Your description was dead on! I started with the junction of the supply takeoffs with the main, and each one had a significant area to seal. As well, each takeoff damper had a large hole, and then the elbows. The dirty insulation was the proof, as you mentioned. In addition, I sealed the joint at the supply plenum/main and each joint down the main.

My next task is the supply boxes. I inspected one that was near by, and noticed almost no dirt on the insulation. If I find this to be the case on others, I may not take the time to seal these, because access is much harder (distance, insulation, low/no head clearance) and they don't appear to be leaking as significantly.

I'll let you know how things go!

what is "Mastic"? Tape or some sort of paste sealant? How does it come packaged? In pails of.......? General cost and what application tool do I need to apply it?

Thanks for your help.

Robert