Not everyone is motivated by money.
A very large proportion of people in jobs are, because the purpose of a job is to earn money. The railway probably does have a higher proportion than say Tesco's tills of people who have built up enough money to retire and are simply continuing to work because they enjoy it, and with the ageing workforce there there are probably more of these than there were, but I suspect that to some extent every man* has his price.
* And woman obviously. Not deliberately discriminatory, just that that's what the old saying actually is!
For some people you would really have to jack the overtime rate up to something quite crazy before they would even consider doing it, and even some people still wouldn’t. I wouldn’t.
High overtime rates for time slots where people really don't want to do it otherwise aren't rare in other areas of business. I seem to recall my mother used to do Boxing Day in a bank call centre for quadruple time plus time off in lieu, which was enough to be attractive. Though she wouldn't do Christmas Day for any money, I think they were offering 6x time for that and did get enough people that way (often it would be those from families who due to religion didn't celebrate Christmas, but there weren't quite enough people in that position to get enough at a lower rate).
One could thus argue for a higher overtime rate during school holidays, but one could also see that the unions might head towards industrial action there as it disadvantages parents.
But beware the idea that people will do overtime if the price is right. Yes people will, but a proportion of these will then go sick for their normal booked shifts. So apart from costing a shed load of money, it has started a vicious cycle where you now have to pay a load of OT at your highly inflated rate in order to cover those now-uncovered shifts which wouldn’t have otherwise been.
Obviously you'll get people who very occasionally are in that position because they just didn't sleep well the night after the overtime, perhaps because something particularly stressful happened. But if particular individuals persistently do that aren't you getting into disciplinary territory there (or at least refusal of overtime), as if that person knows they are likely to end up calling in sick the day after doing overtime due to tiredness, then they have made a particularly poor judgement repeatedly and knowingly on an ongoing basis?
OT works when people are being paid a rubbish wage so they have to do it just to put food on their table or pay the rent, although the moral rightness of that is a separate discussion. It’ doesn’t work so well when people are being reasonably paid, and all the more so when you have a safety critical role where you don’t want people turning up burned-out.
This is a good argument not to rely on overtime, though the effect of this in this case would mean you would need to give less time off during the school holidays, which I again suspect would lead to strike action.
Given all this, therefore, is perhaps reducing the timetable (particularly peak extras) on a planned basis the way to go? At least people can then plan, and unlike where it's done with random cancellations based on who shows up you can max out train lengths so capacity is maintained as far as possible. Though this isn't always done well - for instance the planned Avanti cancellations have left MK with a very poor fast service to Birmingham (some three hour gaps) as they've just lopped a few diagrams out rather than going back to working the Scotland service in the slow path south of Birmingham.
As an example, for the WMT services on the south WCML, might it work better to run basically an all week Saturday timetable for the 6 weeks of the holidays? That is, just the base 2 Birmingham, 2 MKC, 2 Tring and 1 Crewe, but with everything 240m long except the Trings for which 5.730 would probably be OK? Or even lop the Trings out too other than from 0600-0900 and 1500-1900? Commuting during the holidays is down so much that this would likely have enough capacity, and if you're lopping some Avantis out too not being able to use 8-car P10 at Euston shouldn't be disastrous. The longer off peak trains will also help for the higher leisure demand.
And as for Avanti, surely reverting the Scotland to the slow path south of Birmingham is better than just randomly lopping a few diagrams out of the semifast? That way MKC doesn't lose a chunk of its service, and removing the whole second fast service will presumably save as many crew diagrams?