With regards to weight, my friends here in Austin (that run a company that specializes in ICE-to-BEV conversions) tell me that the most important thing is to maintain the relative distribution of weight between the front and rear wheels.
Cars are designed to operate in a certain range of weights, as they get loaded with drivers, passengers, cargo, etc.... so long as the distribution is roughly the same, then the careful tuning of the suspension and handling, etc... should all still mostly work the same.
Sure, it might be a bit more sluggish if it is significantly heavier, but that should be about it. You might b able to largely solve that problem by just putting some stronger springs in the suspension, which might already exist in the third party market for other people who are doing other kinds of work on the same type of vehicle.
Of course, you’ve got to actually do the work to make it right, but keeping the same basic weight distribution will probably solve at least 80% of the problem.
With regards to components being really heavy, consider that the engine and the transmission are two of the heaviest components in most any car. If you can eliminate those in your BEV conversion, that gives you quite a bit of weight to work with for the new heavy components.