Ned:
I'm always happy to serve as a bad example. I did what you're suggesting and have regretted it ever since. Do yourself a favor and buy a dedicated bullseye 1911 wad gun first. If you don't, you'll end up with one anyway, in the future.
My recommendation is that you look at the Les Baer or Rock River wad guns. Yes, they are more than you are budgeting, but you will be getting what you need, and ultimately what you want. Adding a red dot is up to you, but I am certain that if you stick with the game for more than a year you will be wanting a red dot sight. UltraDot sights are excellent and have an excellent warranty.
I started with a Kimber Gold Match and it was fine for about a year, then I started looking at wad guns and bought one. The Gold Match sat unused for years until I revived it as a Marvel .22 conversion.
If you are firm in your requirement to stay within the budget, try buying a used wad gun from
www.larrysguns.com,
www.pilkguns.com, gunsamerica.com, or one of the other gun auction sites. Some of the shooters in your leagues may have guns for sale.
I shoot that 45 a lot, and you'll need to shoot yours a lot to get good at it. It will be well worth your while to use a gun that is made for the purpose.
Avoid Clark Custom Guns unless you like hassles and inferior product.
If you have further questions check out bullseyepistol.com. There is an e-mail based forum that you can join and you will be able to ask questions to an audience of bullseye shooters.