£1000 is plenty of a decent budget experience, especially as like you say you have decent control over the environment. Basically you will have to decide which compromise you want to make, if you go for a DLP option you will likely get better contrast and black levels but may be limited by resolution and less than great motion handling, or a route like Epson where you can get reasonable 4k rendition (albeit not native) however the contrast will suffer. It would also be worth understanding what you plan to use the projector for, 4k really looks good when projecting a large image, however if you are looking for more gaming orented I wouldn't go down that road!
I personally ran a budget Epson EH-TW3200 for 8 years or so and really enjoyed it. I recently moved up to the EH-TW9400 as my budget had increased somewhat but I did consider the Epson EH-TW7000 and for that money that is what I'd go for personally. There are some decent DLP budget offerings but none of the sudo-4K ones are that cheap so that's why I'd opt for the Epson.