IMHO you would be better off with a van a little too big, rather than a little too small.
Sounds like you’ll have riding gear, other luggage, etc. as well.
A long wheel base, semi high top, Ford Transit, or equivalent would be far more suited to the task in my experience.
The advice to use a couple of front wheel chocks is also good, not strictly necessary, but it makes the job a lot easier, especially if you’re not too familiar with transporting bikes in this way, and it reduces the risk of damage significantly.