I tried to answer your question in the kitchen forum but it said I was spamming. If you google warmly yours they have an online calculator. It worked well for us. I am retired & not at all connected to any company.

If you already have a boiler and hydronic heating in your house, it makes sense to tap into the existing system and heat the basement off the same boiler. Your cost for heating the basement will be only incrementally higher than what is now costing you to heat the rest of the house. Electric heating in the basement would would probably cost many times more. If the heating guy who gave you the $2900 price is the same guy who installed your boiler or heating system, then it probably makes sense to have him do the work. He knows the system. You might ask him if there's any other way of tapping into the existing system that might cost less. Perhaps running baseboard radiators that begin on the wall enclosing the boiler room (I'm assuming your boiler is somewhere in the basement), or something else. If the heating guy is someone that hasn't worked in your house before, then why not get a couple of other estimates from other firms. Another outfit may offer a better solution that's less costly, or perhaps, just have lower overhead and do the work for less. Since you plan to be in the house for many years, I'd encourage you to avoid the electric solution. What you save up front will probably cost you much more in the long run.

I've used Warmly Yours in my foyer and a down stairs bathroom. It works well. I used hot glue to tack the mat to the floor. Then skimmed a light coat of thin set. The next day, I used unmodified thin set and put Ditra over the Warmly Yours mat. I would use Dirta because it's an anti-fracture membrane.

Mike, it sounds like you're looking for a broad area solution that will cover and heat your entire basement, much like a centralized forced air system would. This approach may not be in your best interests, or even desireable. One of the beauties of electric heating systems is that they allow you to easily create zones. You may have a room that, due to factors such as sun exposure; prevailing winds; uneven insulation; etc., may have a much greater heat loss, and therefore be harder to keep warm, than your other rooms. You may also have a room or rooms that are not continuously or currently occupied. Why waste the energy to keep them as warm as rooms that are occupied? By having a separate thermostat for each room or zone, you can easily tailor your heating as needed, and the result will be much more consistent temperatures from room to room (if that happens to be your goal). Just a thought. :-)