Lodestars are pretty good – 1st gen is probably good enough, as is the ZWO ASI120mm. I’m considering those for my camera to do a similar thing. Saw a second hand Lodestar today for £150 and the ASI is similarly priced. A significant part of the cost would be the lens on top… I will probably control mine via a Raspberry Pi.
I use a QHY5L-II with an all sky lens (type supplied with ASI120) this gives full coverage of my observatory when running remotely, I use Sharpcap to control the camera.
I have a Raspberry Pi zero with a Pi NoIR (sic) camera in my observatory, but it is not really sensitive enough to show anything. I bought an IR illuminator and the combination works well.
Of course you don’t really want to use an IR illuminator (as you already know) as the cameras might pick it up.
I only use this if I want to film something, not for normal observing.