A couple of questions on excesses:
1) Should they always be done before travel, where possible, if boarding when or where the original ticket is invalid. Or are most conductors reasonable if you're upfront about having the wrong ticket?
Depends on excess type.
For over-distance, it's very important that you do, because if you are caught beyond the validity of your ticket - where there
was opportunity to pay before boarding - then the only excess they can do is to the full Anytime fare, or if cheaper issue a new ticket from the last station your ticket was valid from. Even if you ask for the excess
before your ticket runs out,
some guards will only give you the choice of getting off the train (and it is highly likely you'd then have to get the next train) or issuing a new Anytime ticket or full-price excess. There is no good reason for that, IMO, but the rules allow them to. But, as you say, most guards will do it, and if they don't you can always get off the train before your existing ticket runs out.
Standard Class to First Class is variable and depends on the operator, in general this should be done before boarding but some advertise that upgrades are available on-board at no cost (in which case an upgrade is likely to be cheaper than an excess anyway).
Change of route and change of ticket type attract no penalty to be done on-board, but if there are barriers then barrier staff may insist on issuing the excess before you can board, and this could mean you miss your train at some stations (e.g. Euston), if there
was opportunity to pay before boarding I
don't think you could demand to be allowed through the barrier to do the excess on board.
If there was no opportunity to excess before boarding then the rules on board are identical to the ticket office.
2) I was told at Liverpool Lime Street that my Liverpool -> London return could not be excessed to return instead to Birkenhead despite the fare being the same. Was that correct?
Nope, they probably didn't want the hassle. Ask at Euston on your return.
Note that some people claim (and I can't find anything that proves or disproves this) that once you reach your final destination you can't excess the ticket, as the ticket has expired. Obviously such a claim only applies where there was opportunity to buy before boarding. I wish I could disprove this but I have no documentation either way.
It is difficult to find good ticket office staff who will do excesses correctly. It is not uncommon for them to refuse, or do it wrongly (sometimes undercharging but more often, overcharging).
In general guards do a better job of excesses, in my experience and also based on what people have reported to me. It also varies by route, TOC and location.
For example, if you try to obtain the excess at Euston, you will find the very best most knowledgable (and polite) staff work for LM. But, equally, the very worst and least knowledgable (and rude) also work for LM. So it's down to luck of shifts etc... Virgin are in-between, with less extremes. St Pancras and Marylebone are better for excesses. In general EC is good, but King's Cross isn't up to the usual EC standards. But I know 2 people who were refused excesses at King's Cross, insisted on seeing a manager, and successfully obtained excesses (and the staff member got a telling off for wasting the managers time)