I like my DA 35mm f2.4, but I do not have K-1. Maybe you might prefer FA 35mm f2 (made for FF sensor, but older. Same optical lineage as the DA 35mm f2.4) or Sigma 35mm f1.4 (big, heavy, but very sharp). There is also Samyang 35mm f1.4, but it has no AF. But it is Sharp and affordable, and it has A on aperture ring. Pentax FA 31mm is another good choice, people like it a lot.
Does the Tamron have an aperture ring? If yes, you can still use any aperture you want. You just have to set it by hand and use M mode with fixed ISO (not Auto ISO, not ISO range). A setting on aperture ring means the camera can set the aperture. Menu --> Enable aperture ring (very end of menus), and then M mode with fixed ISO. All other modes will default to "Av mode" which will only shoot wide open aperture. you can see if camera switched to Av mode on the back LCD.
35m and 28mm on K-1 would be good for Iceland. I would also add something like DFA 100mm macro (you can buy used, it is a top lens at a good price)
Pentax A 50mm f1.7 another affordable FF lens:
https://www.pentaxforums.com/lensreviews/SMC-Pentax-A-50mm-F1.7-Lens.html
When I travel, I usually have three lenses. One (very)wide, one normal, one telephoto. That way you have almost everything covered
We had threads about Iceland trips before, you might want to search the forum.
Tl;dr: I recommend you take 28mm, Pentax A 50mm, and think about Pentax DFA 100mm. Maybe add FA 35mm or DA 40mm limited or FA 31mm limited (if you buy 31mm, you probably don't need 28mm; if you buy 35 or 40mm, then 28mm is significantly different)