I'd park on Sefton Street next to Brunswick railway station (on the Northern Line) where there are no restrictions. Two stops in the Southport direction to Moorfields Station and a 10 minute walk west along Tithebarn Street straight onto the boat.

Trains run every 15 minutes between about 06:30 and 23:30 (half-hourly on Sundays), so you don't even have to worry about missing "your" train. Single fare is about £2.50.

It's my route to the TT every year.