I don't think you can cast any type of latex rubber in alginate at all, brush on or pour in. Latex is liquified by a solvent, which needs to evaporate out in order to solidify. Alginate is powder and water, so it's wet. Latex isn't going to dry at all inside the wet alginate mold.
You need to use either a gypsum based material that hardens in the presence of water (like plaster or dental cement), or possibly some type of chemically curing material that actually hardens, and isn't inhibited by the presence of water (like epoxy resin maybe). You can't even use polyurethane casting materials (like the Smooth-On casting materials most people use), because polyurethane is extremely sensitive to moisture.
If your buddy is worried about $40 being too much, you're really backing yourself into a corner. This stuff simply isn't cheap (not $10-20 cheap, anyways). Is there something else you could do, that might not be as good as rubber, but work for your needs? Maybe make do with plaster, or maybe wax? I'm trying to think of something else, but can't really come up with anything.
EDIT: I poked around online and couldn't find much of anything to suggest you could cast rubber in an alginate mold. You're tiny budget makes it really tough. One thing I thought of, you could maybe make a
wax mold of your hand, instead of alginate. I've done it before, but you'd probably have to get creative to avoid spending much money on wax, because you typically do it in about 2qt of melted wax which is going to bring you right back up to spending money. The advantage of the wax mold would be that you could cast inside it with latex, in multiple thin layers (which would take forever, because you'd probably need 20 coats, each taking several hours to dry). Keep in mind that if you try casting inside wax with something that generates heat though (plaster, polyurethane, etc.) you might melt the mold, even if you cooled it from the outside with ice water.