I'm looking at buying an annual season ticket from Peterborough to London valid for LNER. Obviously this would normally be to London Terminals, but could I buy it to London Thameslink (Blackfriars specifically), so I could get to King's Cross then hop on Thameslink from St Pancras to Blackfriars?
The ticket from Peterborough to London Terminals is, of course, valid to St Pancras, King's Cross, Moorgate or Old Street. But it isn't valid through the Thameslink "core". There isn't an "Any Permitted" fare defined from Peterborough to London Thameslink, however. So you'll need to get a different ticket, or combination of tickets, to travel through to Blackfriars.
Using the National Rail season ticket calculator I get "Great Northern / Thameslink Only" options if I put the destination as London Blackfriars. The only "Any Permitted" ticket is London plus Zones 1-6. Using the LNER website doesn't show any valid tickets at all. Is this something where the websites won't show options that the ticket office staff may have?
This is correct - unfortunately there are no "Any Permitted" tickets. The small discount offered for "Great Northern / Thameslink only" tickets is really not worth it here, given the loss of ability to take the numerous fast LNER services that run in the morning and evening peaks. The ticket office staff don't, in this case, have any other through fares that aren't displayed online (though occasionally this is the case, e.g. Boundary Zone fares can't be bought online).
I think the cheapest 'obvious' way of making this commute would, therefore, be to buy a combination of tickets - i.e. Peterborough to
X, and
X to London Thameslink. "Any Permitted" fares to London Thameslink are defined from all stations
south of Peterborough. I've had a look at the optimal combination and it would appear that it's Arlesey in this case. A combination of a Peterborough to Arlesey season and a Arlesey to London Thameslink season would cost £184.40 per week (with the usual provisions for monthly, annual etc. tickets).
Because you're combining a season ticket with another ticket, with the origin/destination of the tickets adjoining, Condition 14.2 of the National Rail Conditions of Travel entitle you to be considered to be making one journey, as well as to take one through service - even one that doesn't stop at the changeover station - so long as you
pass through the changeover station.
The same applies if you wanted a Zones 1-6 Travelcard (e.g. if you ever travel on the Underground or other rail services within London on a regular basis). Arlesey appears to be the optimal 'splitting' point, and the cost is £210.40 per week.
You should be able to buy both season tickets from any ticket office at the same time, however it may be beneficial to purchase them through a website like TransPennine Express, as this will give you an itinerary. This itinerary may be useful, for example, to demonstrate the validity of your season ticket from Arlesey to London Thameslink via King's Cross (something that may be argued not to be the case).