Gut feeling is it sounds like you might be pushing your luck - doesn't allow a lot of recovery time if anything goes wrong.
Rail replacement buses are subject to traffic jams (relatively unlikely that early on a Sunday) - and the railway people involved in their planning tend to expect them to take the same amount of time to get from A to B at any hour of the day on a Sunday, which traffic conditions mean is rarely possible - sometimes it means daytime buses are always late, sometimes it means early morning / late evening coaches tend to run early.
They generally won't hold a train for a late running rail replacement bus (they might if it's the last journey of the day.)
Breakdowns can happen even to the best of operators, and a lot of bus / coach operators are short of drivers at the moment, so the chances of a duty not being covered are possibly higher than they used to be.
When FCC ran the Thameslink lines, their rail replacement bus / coach operations would usually have a spare / stand-by coach or bus somewhere in the mix, usually at each end of the route, so a missing coach could be covered and the public wouldn't notice the difference, although a breakdown would take longer to rescue. I haven't encountered a GTR Thameslink rail replacement operation, so can't say if they still do the same.
I'm not expert on rail ticketing, but I suspect the reservation / journey specific bit of your ticket is for the Kings Cross to Lincoln bit. How about starting from Cricklewood half an hour earlier? (if there is a journey half an hour earlier that is.) I'll let others comment on whether that's acceptable - I can't imagine a rail replacement bus driver / controller would bother about time restrictions on a ticket, but I would not want you to have bother at W Hampstead or St Pancras Thameslink.
Alternatively (and I realise there will be an additional cost to this) are there any direct TFL buses from Cricklewood to Kings Cross? (NW London isn't really my speciality and I'm not quite up to date with recent TFL bus route changes) - or get a bus round to somewhere on the Northern line or Jubilee line and change at Baker Street (assuming they haven't got engineering work as well.)
If the Thameslink train is not available, the next best way for me to get to St Pancras is to take a bus 16 / 32 / 316 / 332 to Kilburn, get on the Jubliee, then change at Finchley Road for Metropolitan. However, as a bus is involved, I'm also subject to traffic instability as well so I decided to rebook my train ticket rather than taking a refund and buy again from St Pancras.
The rail replacement bus and also the train from West Hampstead Thameslink to London St Pancras are unreservable, so I can take any reasonable connection.
I'm thinking if the C11 bus route can be a fallback in case the rail replacement bus doesn't show up, as it runs on the same route to West Hampstead Thameslink, but the timetable doesn't seem that I can do it this way (08:40 then 09:00). However, Google Maps suggest that if I get back to Cricklewood Broadway for the route in the first paragraph I will still make it on time, getting to Kings Cross at 09:21.
However, if the rail replacement bus do turn up late, I can still take the 09:07 West Hampstead - 09:23 train as a fallback, but it will be too late if I miss the 09:07 West Hampstead train.
I will get to the train station first, however, if the bus doesn't appear on time at 08:42, what will be my best chance to make my journey on time?
1. Continue to wait for the delayed bus, hope it shows up on time for the 09:07 West Hampstead train.
2. Get back to Cricklewood Broadway immediately, hope that a 16 / 32 / 316 / 332 bus shows up on time and take the underground afterwards.
3. Run 2 km to West Hampstead station for the train, and hope that the road is flat enough for me to run at 9 - 10 km/h such that I can arrive the station before the 09:07 train.
