OK, looking at the options for a 4-5 week run. I'm basically assuming it'll run for 4 weeks Sun-Fri then Sun/Mon to finish up. However they do it they need to begin evictions no later than the end of week 1.
Weekly Format
If they tried to stick to a weekly format for me that doesn't work, but they could say do two single evictions, two double evictions and perhaps throw in a bonus midweek double eviction (or BBUK "backdoor eviction" if they really want to piss off viewers) which would evict 8 people. If they started with 12 HMs that leaves 4 in the final. Workable, but would feel really rushed - but has the advantage of with live shows generally being only Sunday and Monday the rest of the week you get "pure" Big Brother with the daily shows.
Twice Weekly Format - 6 nights a week
For me with such a short series you have to run two weeks in one, though you'd still wait a week for the first eviction. From the second week I'd then do evictions on Sunday and Thursday with nominations on Monday and Friday. I'm pushing noms to Fridays as it gives them excuse not to do FNL (not time for it in this format) but also means viewers get at least Tue/Wed as pure daily shows, and to an extent the pre-eviction daily show on the Thursday too. I'd run the daily at 7pm before live shows then at 7.30pm on other nights - the new 10 schedule gives them the flexibility to do that. This gives them 7 eviction shows - I'd assume 3 might be doubles so if you go for 4 in the final that's 14 HMs.
Paired show Format - 4 nights a week
I think the promo suggested it would run 6 nights a week (but it also suggested "bigger and better" IIRC) but if it just ran 4 nights a week I'd run it on Sun/Mon and Wed/Thu - the first show would include the nominations and the second the eviction. Whilst I'm not convinced this absolutely works with the traditional format (but could work well with the US format or Seven format) it might be better to basically rethink how the show is scheduled rather than try and make a 14 week show fit into a 4 week timeframe. (Uncut could give them a show on Tuesdays in a later slot or just streamed)
We're basically looking at the Seven structure of the show, but doing it live and with a traditional nominations process. This might work better with the idea the show will be around on streaming for months after it finishes. You then work in additional tasks to each episode - presumably for the weekly budget and ad-hoc rewards rather than related to the power to influence nominations. Whilst you could have US style elements I think in the time frame available that would be too complicated for a "pilot" run. In this scenario you'd have 18 episodes over 4 weeks 2 days with an eviction every other episode. You'd probably skip the eviction on day 2 but can add another one in the day before the finale so potentially 8 eviction shows, perhaps with 3 doubles again so that's 15 HMs.
Ultimately though the show would have a much better schedule if they just gave them the time it really needs - I'd say 8 weeks as a minimum, but the threat of a 4 week series suddenly doesn't make 6 weeks look so bad.