We got married for around $1800 (although that was in 1997 so I guess you've got to allow for inflation, lol).
We also paid for it mostly ourselves (my Dad chucked in $500 and DH's parents helped with food etc) and did it all in 8 weeks - like you we didn't want a long engagement, we just wanted to do it

My dress cost $300, we hired DH's suits. One best man & one maid of honour, she wore her graduation dress (we were only 2 1/2 years out of high school).

I bought flowers from a florist but didn't tell them what it was for (ups the bucks straightaway!) I had a stem of orchids, it was gorgeous & cost around $20.

DD1 & my sister were flowergirls, mum made their dresses.

Mum's DP was a professional wedding photographer, so that was a big saving.

We bought our rings for $50 from Cash Converters

Wedding was held in PILs backyard, they had a rainforest kind of area which was very pretty. Reception was a buffet / barbecue type thing afterwards. Everybody ate drank & had a great time

and, if I had to do it all again, I'd do it all the same, bar a few small details. I have been to some big weddings over the years, and they are lovely (my sister's wedding was am-aaaazing!) but for me I couldn't justify the cost.

As for a registry... I don't understand why not? It's your wedding ... if you want a registry but not all the other trimmings why on earth shouldn't you have it? maybe I'm missing something, lol.
Another idea though is to have a wishing well, you could send out envelopes with your invitations and get people to make a donation. I know there are some lovely poems for the wording of this kind of thing...just an idea.

Anyway Congratulations! wishing you much fun & excitement in your planning, & a long & happy marriage