Others are saying that bell peppers have no taste -- but I'd disagree. The green ones have a kind of grassy quality to them.
Obviously, there's wheat grass, but I never have that around. There might be some herbs that could pull it off (eg, flat leaf parsley; maybe taragon, but also gives a licorice note)
You might try some dark greens ... spinich, kale, swiss chard. They've got a touch of other stronger flavors to 'em, but if you cook them down first, you might be able to tone them down some. (I guess you might describe it as a 'spiciness' ... it can be a sharp flavor.
... for the texture, though, my first thought was bok-choy. It's actually a cabage, and it has some dark green leaves, but the thicker white parts have that watery/crunchy quality that other people have mentioned about bell peppers, but there's that sharp cabbage note that might keep it from fitting your requirements.
update : okay, as the issue is specifically fried peppers, you're going to be bringing out the sweeter notes of the peppers, which you're not going to get from a cabbage. Sweet onions might give some similar qualities (once fried well), as the cooking will mellow the oniony qualities, but the sugars will caramelize.
You can also try looking for jarred peppers -- they're usually packed in oil or a vinegar solution after being roasted. There are 'hot' and 'sweet' varieties, where the hot ones also have some hot peppers in there. The non-vinegared ones sweet ones might work for you.
Also, remember that bell peppers, like most vegetables are a seasonal item -- if you're in the north, it's the end of winter, so any peppers are being being grown in hot houses, or brought in from the southern hemisphere, which jacks the prices up.
The classic substitute is margarine.
Most brands are vegan, which would meet your non-dairy /non-meat requirements.
As far as taste and mouthfeel goes, I suggest either trying out a few brands or checking some vegan blogs from your country or region, there is a difference between brands but some are reported to be remarkably close - whatever that means.
Best Answer
In regard to the issues you've had with the Toffutti Sour Supreme...wait until you take it off the heat and stir it in right before serving.
If it still breaks, then try stirring arrowroot powder, tapioca starch (avail. in Asian markets), or potato starch (about a tablespoon per cup of sour supreme) into it before adding to the stroganoff. These starches (amylopectin) have a lower gellation point than grain-based starches (flour, corn, rice) which are higher in amylose and require heating to a higher temperature for the starch granules to swell and pop, releasing their starch.
OR
Try this recipe for kosher beef stroganoff where they're using coconut milk for the kosher cream sauce and say that the coconut flavor doesn't come through in the finished dish.