That's not really possible, so I'm afraid you'll have to wait until your USO quote comes back.
Firstly, the distance to cabinet is not useful; distance to fibre aggregation node is what you need. However the locations of fibre aggregation nodes are not published!
Secondly, there are no standard price-per-metre rates for these things in Openreach. What comes back is what comes back. The costing model is completely opaque, with aggregate line items for "civils" and "stores".
The biggest factor, which is in your favour, is the demand aggregation - this assumes that 70% of the properties to be covered by the install will take it up. For example, if your FTTP CBT will serve a cluster of 10 USO-eligible properties, then it's assumed that 7 of them will take service, so BT's contribution will be 7 x £3,400. That may make it completely free, or it may still leave a huge excess. See BT's report
here.
Therefore I could guess "free to £30K", but that doesn't help you much. And even the upper limit of that is not guaranteed. It depends hugely on what the surveyor says needs to be done.