Can't you use youraddress.servicename@gmail.com? I thought gmail strips whatever comes after the dot. (I don't have a google account, so I could be wrong or maybe it was a different character, but I remember reading about it a couple times on here.)
It ignores periods so you could also use your.address@gmail.com or y.ouraddress@gmail.com or whatever.
Some sides block plus addressing but that's what I use a lot of the time.
Gmail ignores dot characters. y.o.u.r.e.m.a.i.l@gmail.com is equivalent to youremail@gmail.com
yourname+servicename@gmail.com
From my experience, many (bad) websites consider "+" an invalid character and prevent you from using the address in this form.
Smart spammers can just strip the service name since it works the same for all Gmail users.
Really need dedicated addresses like Fastmail's Masked Addresses.