Essbee - I am not sure which MPPT solar charger you have, but some (most?) will have a button and you can scroll through various pages in the display.
So if you have something tha looks like a panel and a voltage, that will be the output voltage of the panels, you don't want this page. You probably will have a picture of a battery and a voltage. That is the page you are looking at and tells you the battery voltage. So if you do have a page like this you can measure the battery volts. Probably this is the 13.7 you mentioned, in which case I think your batteries are ok. In bright sun I would expect something like 14.4v as they are now charging.
If it is very dull sky/dark that is then the resting battery voltage. What does it say?
Note - If you want to connect your charger as a fixed installation then using crocodile clips will fail your next safety inspection. But it is fine to connect it and use it from time to time.
I also have about 400W of solar, and they keep the batteries fully charged when I don't use the boat over the winter months.
The engine start battery should be ok for a couple of months, any longer and a couple of hours charge should keep it in good order.