Hallo Kurt,
according Three Decks the Sovereign o t Seas had this armament
View attachment 149281
British First Rate ship of the line 'Sovereign of the Seas' (1637). Dates of service, name changes, previous and next incarnations, dimensions, armament, commanders, officers and crewmen, actions, battles, sources
threedecks.org
So they used on the Forecastle etc. only Culverins, and I am pretty sure very small ones.
The shown barrel is one older one, which is very similar to a swivel gun, so it could be, that they had carriages with only one axis. They were relatively easy to move, due to the fact, that these guns were not very heavy, and also had not so big repulsion. So I think it is worth to search a little bit more about these carriages.
Nevertheless John McKay is showing them with four wheels. Take a look at Nigels Book Review
Sovereign of the Seas by John McKay 1637 Part 1 Hardcover:296 Pages Publisher:Seaforth Publishing 3rd March 2020 Language:English ISBN-10:1526766299 ISBN-13:978-1526766299 DIMENSIONS:254x295x25mm RRP:£40 SYNOPSIS Sovereign of the Seas was probably the most lavishly decorated warship ever...
shipsofscale.com
Maybe this book would be good for the research and for the bashing of your kit