Senora,
Didn't see this till just now, but I would have been advising a tentative go for it, so I am pleased it looks so positive. How exciting !
You can turf whenever it's not frozen, and it's better, I think, to turf when it's cold than when it's hot as the turf won't dry out so quick and die.
I laid turf last year from Coronet Turf - a farmer turned grass specialist who grows 'soilless' on s clever woven substrate thingy so the turf is much lighter but with fantastic roots. Quality is second to none in the UK, and I am a total plant snob.
Phone 'em up and check it will take your predicted wear - kids will kill finer seed mixes without sufficient 'harder' grasses like creeping fescue (I think)... it might be better to get stuff from B&Q etc. as it is tougher. I think their supplier is Qlawn. Whenever I check their stuff though it is so much poorer than Coronet's...
(They are in Basingstoke but courier to anywhere in the UK. I have no connection except as a previous customer).
I think a reasonable landlord would cover the turf if you lay it. Turf is reasonably quick to lay, but the soil prep must be immaculate, and you must be sure not to walk on it for as long as possible.
Ref: Other challenges...
Air Con: B&Q have some cheaper machines on special at the mo. Maybe grab one or two for the most important areas ?
Alternatively, if air con is in your 'must haves' for a future house, you could explore a fitted system designing it with the shortest possible duct runs so it can easilly be ripped out when you move.
Satellite: Could you contemplate ditching Sky and getting Freeview and saving 400 quid a year ? You'll be able to satellite the dish in the garden, at a low level instead of the house maybe ? Possibly run a conduit at the same times as the lawn ? Easy to remove later too...
Stud Walls: Get a chippy in for the day. (Whereabouts are you ?). Depending on joist accessibility / heating in concrete floors etc. a chippy can accomplish major stud wall antics very quickly, particularly if you don't need to liaise with a sparky for socket positioning etc. If it is temporary, you might not need insulation or even plastering, just depends on how immaculate you need everything. Do you need shelves in the basement ? If yes > integrate into stud wall uprights for incredible strength and v. quick build.
HTH