Chritensen, Patriot Valley and MPA all have fantastic turn keys for under 2k, but customer service, if anything should go wrong, is very hit or miss from all three. In today's market where $2,500 can build a very very nice semi-custom and if you're not trying to make production class I don't think they are worth the potential headache.
Going with a Bravo Chassis($350), Trued 700 ($450) from Northland Shooters, Criterion barrel($300) and trigger tech($150) puts you well under your budget and despite forum blow hard opinions is still a great combo. Prices listed are all without tools, shipping and FFL transfer fee so keep that in mind if they need to be included in your budget.
There are lots of options to upgrade action, chassis or barrel to the brand of your choice within budget. For example a Big Horn action is $825 and they work with Savage small shank Criterion barrels($300). You could even spec out a nice custom manners stock w/ mini-chassis to go with the Origin barreled action and come in very close to budget if you're careful with the stock add-on options. Though with tools/shipping you're likely stretching the budget some.
The issue you're going to run into, the thing that can get super expensive, is the weight. If 7-8 is a hard goal, the above combo is already pushing the weight limit. Bravo is roughly 3.5lb, action/trigger is roughly another 2lb and 24" sporter contour barrel is right around 3lb. So the real question to ask yourself is how committed are you to the weight limit?