Check out electric boilers. They are made for heating and available in all sizes.

But isn't electric heat the most expensive to operate over the long haul?

its not advised to use the same water for mixing domestic and space heat. the tankless is a good way to heat up the floor and baseboard for the basement. it will only fire up for the temperature rise that you have it set for. I do have one queation. Why don't you make the new basement that you dug out radiant also...........?
If you want you can put a heat exchanger on the water heater and use it for both domestic and spasce heat.

Thanks wisehvac! Will take note that it's not preferable to use the same tank.

Good question! The concrete floor has already been poured. Is it even possible to install RFH on TOP of the concrete? Ceiling clearance is an issue, too; right now we're at 7'4". (Any deeper would have required that we lower/replace the sewer line all the way to the alley, which would have meant lots more $$$). So is it possible to still install the RFH over cement and not lose too much height?

I only mentioned electric boilers because you wanted to use a hot water heater.

Electric boilers are 100% efficient, don't maintain any temperature when not in use, don't require cleaning or a chimney, and will probably last your lifetime.

We have this, but to clarify how it works is that the boiler heats two different "coils". One runs through the radiant floor/baseboard radiators. The other runs on a pipe through a water tank which heats the water in the tank. So you have a closed loop of water going through the boiler which radiates the heat either into radiators or into fresh water supply in your water tank ("indirect heating").

We're pleased with our system generally. It provides loads of hot water in part because the boiler water is ~170 degrees and that means we can keep the tank at a higher temperature and then mix it down to 120 for use. In effect that means that the tank is effectively 50% larger or so. Also, a boiler has loads more power (BTUh) than a gas water heater, so you get much faster "recovery" (i.e. reheating) than with a usual water heater.

A couple of drawbacks--it seems less efficient in summer (no surprise) than a standard water heater because you're running a huge boiler just to keep the water hot. On the other hand, in the winter it stands to reason that it's cheaper (no way to test actuals because this was a new system in a new (to us) house). The other is that it means you're relying entirely on your boiler. If that goes out, then no hot water (of course, same can be said if your hot water goes out). The cost was probably higher, because of additional piping, but I think that you recover that in lifespan since there's no burner on the tank itself, and boilers tend to last a lot longer than water heaters.

An electric boiler maintains no heat, so it's zero cost in the summer.

A properly maintained quality boiler can last a lifetime, so in the long run, I would skip the hot water heater option and use something that is meant to heat.

Wow, this is all so helpful!
Still wondering if it's possible to install radiant floor tubes on top of concrete that's already been poured.

Can't you install some sleepers on the concrete that will raise the floor about 4 inches (2x4 on edge plus subflooring)?

Wow, this is all so helpful!
Still wondering if it's possible to install radiant floor tubes on top of concrete that's already been poured.

Yes, you can install pex in a device made for pex over top of concrete, any time you want. Then cover with ceramic tile. It raises the floor about 3/4"

Here is what I would do if I was you. You don't need that many btu's to heat up them two rooms. Plus you want to get hot water also. haved a certified takagi tankless water rep. come to your home. ( this will be free ) tell him you want a tk-3 pro. ( better heat exchange in the unit itself) it can fire up to 199,000 btu's and down to 11,000 btus. then you want to use a bronze bump with a heat exchanger on one side, plus boiler trim. (1/6 horse power. with a mixing valve for your domestic water. you want to then put two zones on other sided of a heat exchanger with a zone board for 2 zones with 2 pumps one for the baseboard. Ask for high trim baseboard so you can set the water temp down and get max btu's per lininer foot. set the temp for 150 degress durring the winter cold month. Now for the radiant floor get a viega dealer in ur neighborhood. get climate panels that you can put cement nails in and the put a flooring on top.
If you wanted to know more about this rout just leave a post.
you can have all 3 comming off one unit. The best thing about this type of set up is that you dont need 180 degree water like a boiler. and in summer time you can set the water temp down to 120 or 115. and when your away on vacation you use no gas.
The down side is hat the climate panels can be expensive, the tankless water heater has to have a nice size gas line. the equipment to do this job can get pricy. I mean really pricey.
with nice equipment comes a good price. Takagi & viega are my brand of choice. but you could use navian and wirlsboro if you wish. all 4 manufactors will be happy to come to your home and sit dowwn and talk to you. ( I sell all four)

Thank you sooo much! I feel so much better about this now. I know this is do-able, and that it will be in our budget. There's been a big learning curve about this topic for me and I can't tell you how much I appreciate it.