I would use a vegan plain yogurt thinned with vegan milk** of your choice to replace the heavy cream, and with an addition of some ground cashews (soak first in some of the vegan milk, then grind to a paste). Many North Indian recipes use ground cashew (or to a lesser extent, ground almond) as a thickener and it makes the gravy richer. (See recipes for Malai Kofte for examples.) This will give you a fairly neutral flavor and stays reasonably authentic.
I think heavy cream is probably being used in your recipe to make a richer recipe (both in cost and texture), the type of thing that might be served at a fancy meal for a party or feast day but not for every day, and a more "every day" style of sauce might have had less cream added or just plain milk or yogurt.
I realize that you're trying to perfect one specific recipe, but I wanted to mention that there are also plenty of Indian curries which don't use any milk products at all to begin with, so if you're catering to a vegan crowd or just trying to reduce use of animal fats, you do have a lot of options that don't start with a cream-based sauce.
And, I know you already said you want to avoid coconut, but apart from that, replacing cream/milk/yogurt with coconut milk is quite common in South Indian cooking but might seem out of place in North Indian food. If you want to try to keep your curry reasonably authentic (or be able to produce multiple styles of curries) you may want to consider developing one recipe with more of a North Indian slant made with, say, almond-milk + almond-milk-yogurt + ground cashew, and a second recipe with more of a South Indian style made with coconut milk for the times when that particular person won't be at the table. :-)
**Most US grocery stores these days have a large selection of alternatives to dairy products, although this does vary regionally. For example, in San Francisco where I work you'll find a lot more options than in Bountiful, UT where my parents live. You may find some shelf-stable milk replacement products near the baking aisle, but most of the ones that are more pleasant for drinking plain or cooking with will be near the regular dairy products.
There is a lot of variation in flavor and quality of different brands, and you may find that soy and coconut based products are the closest to dairy milk. Almond and rice products tend to be thinner. There will usually be some "original" flavor and some vanilla or even chocolate. For cooking you will want "original" flavor, of course. It will not taste identical to dairy milk. In my opinion, coconut-based milk replacements are usually the most neutral and often have a better texture. In my opinion, they don't really taste much like coconut in this form.