I don't like longstrider for this, long-lasting magic doesn't feel right. Longstrider lasts for an hour, do they have to be on all fours the whole time to get the benefits? Also proficiency bonus times per day longstrider seems like a lot, in tier 2 that's 3-4 hours of longstrider, which is often enough to be the whole relevant part of the adventuring day.
I'd tend towards something like they can take dash as a bonus action (maybe prof times per day, but I don't think it needs the limit) if they can free both hands to do 'get on all fours to go fast'. Not magical and doesn't have them going fast for hours on end, and the big dash feels more appropriate than a longer-lasting, constant bonus.