im an installer and i do this all the time. dont be such a chicken (buc buc)
A good quality splitter will have RF isolation between outputs. So, if you hook your modulated channels into the splitter using the out ports, you should only get good video from the In port. Connecting the two back fed TVs to the Out ports of that four way splitter should create high isolation and those TVs would have bad pics. Unless it's a real cheapo splitter, those things even pass voltage when they're not intended to do so.
OP's best option is to connect the two Home Distro ports to a backwards two-way splitter. Then, from the In port, connect that wire to a separate splitter for whole house distribution. Total splitter loss is about 7db with (2) two-way splitters, not bad.