When I built my shop I talked to electricians and called my POCO to get my options. I was in a similar situation, panel full, but I had nothing to swap out.
What I went with was an upgraded service at the meter, from 200 to just under 400. The POCO verified the transformer feeding my house could handle the load.
Then after the meter, the power is split, 200 to the house and 200 to the garage. This results in one meter and the POCO charged $20.00 for them to come out and disconnect service while the electrician upgraded the meter box and meter, then reconnect service.
Similar to what was done at this
link