That might be more complicated than you think. Don't forget the in 5e you up all the xp and them multiply by a factor based on number of foes. Adding in player and then having the table fight two encounters at once is more than double the difficulty.
I'm not so sure -- the math about doubling the XP presumes that the encounter has that number of monsters from the beginning. If an encounter is designed so that it has a certain amount of monsters at the start, then more monsters appear at the beginning of round 3 (say, from a different encounter area which gets added to this encounter based on the size of the party), then you don't treat them as the same encounter -- you treat them as a 'multipart encounter' as noted in the DMG/DM's Basic Rules. You would still try to ensure that the total XP isn't more than 1/3 of the XP the party should earn for the day (unless you're going for a potentially deadly climactic encounter).
Note as well that the difficulty from a multipart encounter is specifically noted as being because the party can't take short rests between them -- so if you're not allowing short rest between the smaller components of a regular series of encounters, they're effectively one large multipart encounter already.
With all that said, it might still be harder than I think -- I should probably put together an example adventure and see if these ideas actually hold water. For instance, rather than combining four encounters into one large multipart encounter (as I suggested in my original post), maybe it would work better to only combine three such encounters, then have the fourth 'move on' to combine with another multipart encounter in another area of the adventure to increase that encounter's difficulty given the party size. I can see that such an adventure would require a DM to be more familiar with the adventure prior to running it, so as to be able to properly implement the proper encounter size for scaling, which could be a drawback.
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Pauper