Hello Jaxo,
I think you mean paradiso which is a fine grained rather porous stone.
It is a mercantile granite which means it isn't actually a granite-geologically it is a migmatite part of the gneiss group. Nothing to be concerned about -just saying.
Sounds like you have had this stone for a while.
Also sounds like you have existing stains-which you may be able to remove. The older they are the harder that will be. Do some research on poulticing or hire a stone refinisher
Anyway-there is no short answer to your question sorry.
First-most brand name sealers are of good quality. Most likely there isn't a problem with the sealer.
The problem is in the application of the product.
Most sealers contain under 10% resin(the material that fills the pores of the stone) the rest is the carrier which is either water based or solvent. Bulletproof has a higher concentration of resins than standard sealers. Just like miracles porous plus which is similar to bulletproof.
These type of sealers will cost more but require less coats then the cheaper products.
The first thing you need to know is that sealers are impregnating-they live below the surface. When sealers companies state that only their products should be used I think they mean initially. It has to do more likely with mixing different types of carrier solvents. Once the resin is cured within the stone I think at this point you can use another product.
So you needn't worry about removing(almost impossible anyway) any remnants of the old sealer which sounds like there isn't much there anyway.
Once you have the countertop clean and free of stains you are ready to begin.
Do a simple water test-a palm sized puddle of water left on the surface for 5-10 minutes then wiped away.
If a darker mark remains you know the surface is porous and will take the sealer.
You can use whatever sealer you like.
Protect any areas you think may get dripped or spilled on.
Pick a starting point and pour some sealer on the surface.
Using paper towel spread it out over a manageable section maybe 3-4 feet wide. Let the product load (absorb) into the stone for 5-10 minutes or so(do not let it dry on the surface)
Then you must remove entirely all of the sealer from the surface of that area.(most important task of sealing)
Leftover sealer residue is an epic adventure to remove.
Then overlap the previous area and repeat the process for the rest of the counter(do it in sections always overlapping)
Remember to completely remove all sealer from the surface.
I would do this twice (2 coats) which I consider an application.
Then wait 24 hours and do the water test.
You should have much less absorption at this point.
You may even have none. If you don't have any absorption your done. If you do then you can do another application(2 coats) using the same process as the first application.
Then wait 24 hours and test again.
I hope this clarifies sealing for you and you now have a better idea of how to correctly accomplish it.
You could always hire a professional stone refinisher to do this all for you.

Stains were removed prior to applying the glass. The glass is similar to having clear plastic over your sofas so there are new stains except around the sink.
There are only some liquid soap dark marks around the soap dispenser.
I have used poultice to remove stains in the past and it worked, but it was so annoying that a few months later there would be stains again. I would have to use coasters and could not set down a bottle of olive oil or a spatula or a cold glass on the counter because they would leave penetrating marks.
Too much effort to protect a work surface that was used daily.
I may try removing the soap stains with poultice again and ordering a new bottle of Bulletproof to see if applying it differently will make a difference.
According to the bottle, the protection is supposed to last 3 to 5 years, but I am lucky if it even last 3 to 5 months.

The sealer did work when I first applied it, but it didn't last.
Is there anything special that needs to be done to make the protection last longer after it's applied?
What cleaners can be used on a sealed counter that will not strip off the granite sealer over time?

To prolong the life of the sealer use a no rinse PH neutral cleaner specific to stone.
Yes it says 3-5 years miracle says 20 years.
I think it depends on use and the stone.
I would say every year at some point do the water test.
If you seal and maintain it correctly you will get maximum life out of it.