Tough one with you being so far away from H4L.
I can't comment on matching pads/bat- done exactly the same for my son (and he's a 'keeper- so that's 2 of everything!).
That said, I completely agree with you on the idea of a "bat fitting". If you're spending that much (or even if not), you want something that feels right. The problem I had was neither myself nor my son had the language to express what we wanted in the bat. We travelled from near Burnley to Wakefield to do exactly what you suggested (and Johnny described). Swing some bats around, talk about how they feel with the batmaker, and generally agree on a spec that we wanted. We go to Warrior (We love Warrior bats, but his reputation seems to be local/regional!), Scott's seem to have an exceptional reputation on the forum- and Leeds isn't so far.
I think the process is worth the time (in fairness we went for the first senior sized bat- I recently bought a spare over the phone because I could just ask for the same again)- obviously others here seem to disagree. So that pushes it back into your court.
1) Can you justify the time/cost/pain in the (No Swearing Please) to visit H4L? If so, that would lead to you getting exactly what you want.
2) Visit someone closer. Plenty nearby (both I suggested are easy to get to for you). You get a bat that feels exactly as you want, but the stickers don't match. Only you can quantify that.
3) Go to a shop. Swing some bats, and pick one you like. Easiest option.
As a final (sneaky) option- don't some bat companies sell stickers? No idea if H4L do or not. Or maybe get some made up? Buy a bat without stickers locally, then add the stickers on to match the kit. Obviously unethical if you were reselling etc, but if it's just to satisfy your aesthetic needs, then why not?