It’s all in the way you position Patreon. I invite fans to join my exclusive community on Patreon if they want to go deeper in a supportive and safe environment. That’s the language I use. It doesn’t feel like selling or begging to me. Perhaps you could adopt language like mine - just tweak to fit your voice.
I read a blog post on Patreon (can’t find it, but will link when I do) that advised creators to use the term “exclusive community” when inviting people to join you on Patreon. Saying, “Sign up for my Patreon” or “I have a Patreon” doesn’t work. Instead, saying “Join my exclusive community on Patreon” or more simply, “Join my community” tends to draw people more.
I haven’t done special offers as yet, so cannot comment on that feature. I did, however, do quarterly challenges which helped boost my numbers (one month I got over 230 new patrons), but I no longer do challenges because I get a TON of new patrons quickly, but within 90-days, most have deleted their pledge.
If I were to do a challenge, I’d try it as a special offer - just to test. You can read more about how I used quarterly challenges to boost my patron numbers here.