We bought a moka pot in Italy that made easily 10 (espresso) cups. It was a long time ago but I see no reason why they would not exist any more. And no, I don't know where to buy them outside Italy. A 10 second google search scored a 6-cup version https://www.target.com/p/bialetti-moka-6-cup-express-espresso-maker/-/A-14655160?ref=tgt_adv_XS000000&AFID=google_pla_df&fndsrc=tgtao&CPNG=PLA_Appliances+Shopping_Local&adgroup=SC_Appliances&LID=700000001170770pgs&network=g&device=c&location=9007901&gclid=CjwKCAjwnIr1BRAWEiwA6GpwNeQKb_c7d-KG3r3ZmWeIM445Vz4ginYjgQQ8UZ2J2fZrxcsWlIGghxoC6lIQAvD_BwE&gclsrc=aw.dsIndeed. My comment about futzing around was mainly meant for the cleanup. But pouring boiled water into a French press is easier than slowly pouring it into into a filter set. No need for finesse. Just pour.
Your example of a stove top espresso maker (I think they're called Moka pots) is actually my preferred coffee maker. Problem for us is that I've never found one large enough to satisfy the morning crave. Even the largest versions only make one decent-sized cup of coffee.
It was never a problem when we had our land home. We'd just toss two or three Moka pots on the wood stove. But boat life limits the number of pots we can easily store, and our two burner stove also limits the number we could functionally use. So a French press is the next best option.
Edit: Just found a 10-cup version. It is more expensive but stainless steel. We actually switched from the original to something like this one because of some lingering doubts of ingesting acid cafe from aluminum: