Liverpool ATC require booking out over the telephone - not on the R/T.
When you're passing your details over the telephone prior to departure simply ask if you can carry out the detail - I'm sure they'll be pleased to oblige.
If they're on 27 then, to assist I suggest you route via Seaforth, skirt along the top of the Zone and 'drop in' to St Helens from the north. Route back to the field using the usual route as shown on the CAA Chart AD 2-EGGP-4-1 downloadable from the internet (NATS).
If they're on 09 you can depart to the north and instead of routing to Kirkby divert towards St Helens. Reverse of previous - skirt along the top of the Zone and enter at Seaforth.
These options would cause minimum disruption.
Just a thought.
SITW