Is it a good idea to shrink prior to a SQL Server upgrade to a new instance
I hope following information will help you to make your final decision.
faster backup times
You will not have a faster backup time.  See this answer by Aaron
Bertrand.

The backup process does not back up empty pages, only pages
with data, so typically, the backup file will be a lot smaller.
One important thing to note: when using compression, the initial size
needed on the destination drive will be the uncompressed size; the
backup will only be fully compressed at the end of the process.

less files to restore when we take a copy of production
You are not getting rid of any files so I am not sure what you are gaining here. Yes you can save your allocated space by shrinking the database.
there will be a lot of residual space after we've completed these deletes, so makes sense to reclaim it (I'm thinking ~30-35GB, so a third of the DB itself)
It all depends, can your company afford to spare 30~40 GB of space for few weeks/Months which you will need anyway.  You mentioned your auto-growth is set to 75MB and it happens 2-3 times a day. Based on this information you will use 30GB space in  in next 4.5 months.
If you are rebuilding index please do not update all statistics after that. Read this.
I will highly recommend you to increase the autogrowth size and avoid growth 2-3 times a day. Read this.