Tbh, I think that a better approach to the problem to the Townshend Acts of OTL would be to change the objective. Don't try and raise revenues, but instead move the debt.
In this case, use the information/receipts/etc to calculate the cost of the war in the colonies. Before making any policy calls, start sending out propaganda to soften up the colonists. Something like "Stronger Together", etc. Perhaps roping in Franklin.
Then make a move to the Governors of every colony, stating that they have a year, in which time they need to organise a common assembly, or some sort of local institution to be responsible for the debt accrued for the colonies defence. (The exact number would probably be debated, but lets accommodate that).
Rope in Franklin who can be the proxy for the Crown and he can argue for an American Parliament - although that might require persuading him to argue for the case of half the costs of the British Forces in the Americas, in an attempt to recognise the costs incurred by the American local governments. It might be wiser to send someone who argues within a maximum remit of an American Parliament or hybrid of that gets the job done, with representatives of their interests sent to Westminster. (I dunno, say 20 that are divvied up in some way, to be arbitrary, rather than do the maths atm.)
If they refuse to organise, the debt as calculated would be marked against each state according to their size, in Londons financial houses, at which point they would each be liable for repayment.
Basically, "You pay half, and organise it, or we'll have it so British lenders consider you owners of these debts, and lend accordingly.
Not exactly a lovey dovey move - but we're not talking about being lovey dovey. Just what can the British get the Americans to accept in terms of the debts of the French Indian War. But you've got to send the propaganda, and make sure that the Colonies don't get to claim this is a burden on the people, but a contribution to the burdens taken up by Britain. Hard message to sell though.