Pentax is so popular now they've sold out. Plenty of Canikons no doubt as nobody wants them.

The DA 15mm is no real use on full frame. Great for APS-C though ! And for the record, that applies to the DA 14mm too.
The Samyang 14mm is fine on the K-1 (as is the 12mm fisheye) and images will stand cropping well. Even the corners on the Samyang 14mm are extremely good and can be considered a steal at under £300. If a zoom is a must the 15-30 is the obvious answer, at four times the price. I purchased the Sigma 12-24mm f4.5-5.6 via the forum but find its edge performance somewhat lacking. Nicely built though so a shame its optical performance doesn't match so wouldn't recommend that as an alternative despite its interesting range on FF.
If the cost of the 15-30 is prohibitive then the Samyang is a hugely viable alternative and is course wider (the Pentax 15-30 has been said to really start at 15.8mm.)
Another lens to consider is the SMC Pentax K 15mm F3.5 (manual everything) but I have no experience of that. However it seems to get a low rating on the US PF site. I'd get one though if it was reasonably priced. It's FOV seems to be the same as the new FA 15-30 at 15mm.
Another new alternative is the Irix 15mm f2.4 for which we are honoured as it is only available in Canikon and Pentax K mounts. JR reviewed it link. However twice the price of the Samyang 14mm but weather sealed.

I found the Chinon 35-70 f3.5-4.5 A series equivalent to be sharper than the Pentax (from a sample of one of each.)

Can you return it or get it checked under warranty? At the price they are it should be more than fantastic. Mind, basically the 24-70 is a rebadged Tamron whereas I understand the 28-105 is a new Ricoh/Pentax design. The 28-105 wins hands down on weight, bulk and cost (it's similar to the DA 18-135) so it depends how important the f2.8 and 24mm of the 24-70 is. Performance of the 28-105 is pretty good as is the 15-30 you mention. They do make a good pairing with a 70-200 such as that Tamron. I'd expect the Tamron to be back to around £499 after Christmas as it was for the Black Friday at SRS. It's a good, albeit heavy option.

Very well put!

It won't ask if shake reduction is turned off.

Just a clarification. When you say manual focus lenses, do you mean manual everything lenses, like the old M and K series, or do they have an 'A' setting for the aperture like the Pentax-A series as these can require manual focussing so would fit your description of 'manual focus lenses' but they aren't manual everything lenses. It might be easiest to say which lens(es) it is.
Something else to try, when you set item 27 on the custom menu to 2 and come back out of the menu, try going back in immediately to check if it is still on 2 (don't switch the camera off.) If it hasn't perhaps you're exiting from the menu without saving the setting somehow. If it does retain it, see if the camera seems otherwise normal now and lets you take the photo. Then if you turn the camera off and back on, has the item 27 menu option reverted back to 1.
If it's reverted, does the camera retain the date and time? If not it could be the internal memory capacitor has run flat and needs a fully charged battery in to restore it (presuming it hasn't gone bad.)

If you've only just bought it and it has proved faulty, can you return it for replacement or refund as not fit for purpose? You shouldn't have to get involved in organising repairs for something you've just bought unless it was from a boot sale or similar, but even then I've returned faulty cameras at those.

I paid £129 for one at Cash Converters to complete my limited set! Mint and boxed.

Focus hit? If not when does it beep :
Otherwise could it be when you're walking backwards to frame a shot to warn others nearby of your presence?