G'Day Mike,
My shed is about the same distance away from our house and I run one of these in the shed:
https://www.ebay.com.au/itm/40193737...id=28035054297
It all depends on whether it can pick up the wifi signal at that distance though, so I have my router situated high in the house with the antennae oriented to punch as much signal that way as possible. If you can get a wifi signal with your phone (even a weak one) this will work. I get about 1 bar on my phone at the shed without the extender and full strength signal with it. If your obs/warmroom is metal clad, try to position the extender at a window so the metal cladding doesn't block the signal (Faraday's Cages and all that stuff).
Otherwise you might need to look at a wifi bridge - a pair of monodirectional wifi antennae aimed at each other and then an access point in the obs.
Al.