If you’re intending to use first class, it will be cheaper to buy a first class Britrail or Interrail Global pass.
Indeed. The ratio between the cost of standard and first class Britrail and Interrail passes is very reasonable - in the region of 1.5x.
But if the OP does want to buy a standard class pass and obtain an excess for an individual journey, they would pay the difference between the 'appropriate' fares based on the time of travel. However, I can see that leading to some perverse outcomes due to the lack of comparable first and standard fares, as the OP alludes to.
For example from Kings Cross to Doncaster on LNER, the excess would be £103.40 at times when Anytime fares apply (£271.50 less £168.10), but it would theoretically be higher at £125 when the Off-Peak First Single and Super Off-Peak Single are valid (£196.70 less £71.70). I think it would be reasonable to expect the excess to be calculated based on the Anytime fares in such a scenario; a 'white lie' that you're going to travel at times when Anytime fares apply would do the trick if it really came to it.
However the OP would probably find it far cheaper to bid for, or buy, an upgrade via SeatFrog if travelling at 'peak' times. Alternatively they could pay the defined onboard upgrade supplement which is available at times when Super Off-Peak tickets are valid, including weekends - this is between £35 and £45 depending on the length of the journey (see
here).
The downside is that SeatFrog requires you to tie yourself to a specific train and to make that decision at least a day or two in advance (if you want to make sure that there is still upgrade availability). Onboard upgrades are also subject to availability, so could theoretically be refused if the train is busy. But that would be my suggested approach.
It's worth noting that whilst upgrading to first class is generally permitted onboard the train with LNER and on other long distance trains (you pay the upgrade to the Train Manager), for short and medium distance operators or trains such as SWR, Southern and Thameslink it is generally mandatory to obtain the upgrade at a booking office before boarding. If you do want to upgrade onboard then I would strongly suggest approaching the guard on the platform before boarding, and asking them if they'll give you permission to upgrade onboard. Of course not all of these operators' trains have guards, in which case you're back to needing to go to the booking office.
