Put any 24mm lens on an APS-C Pentax then the 1.5x crop factor will make the field of view the equivalent of a 36mm lens on full frame. The lens doesn't actually change focal length because it has been put on a different camera body.
A lens designed for an APS-C sensor may not cover the whole of a full frame sensor but its focal length remains what it says on the lens, it'll just get a wider view on the larger sensor! What is likely to happen is that the extra field of view onto the larger sensor will give rise to vignetting, but some lenses may suffer more than others.

Youtube comparison: link

+1
The K-3 shot definitely looks underexposed. Also the K-5 shot would also look more noisy with an equivalent under exposure and given there are several years between the taking of those shots I wouldn't personally place much reliance on that comparison. Personnel, testing equipment, ambient conditions etc. will all have changed in the intervening period.
In any event one has to look at the overall full image, not 100% crops from two very different resolution sensors.

Looking at your equipmet list much of your glass was designed for FF film cameras so the expense of changing should be minimal (presuming it still has the normal K mount.)

I reckon that the K-3 would have had a full frame sensor if Sony hadn't been about to release their new Alpha 7's. Will we see a K-3II next year with the new FF 24mp sensor and a K-3IIs with the new FF 36mp sensor?

One subtle aspect of the K-3 over most other DSLR's is the fact that it has two SD slots. It is possible to have RAW files go onto one card and jpegs onto the other. Should a card go bad there is always a backup of the image on the other card.

Agreed with all that but why not send the lossless TIFF file to the printers?

If you are getting noise, moire and under exposure from a brand new K3 I'd be somewhat concerned there might be something wrong with the camera or the way it is set up. Is the query to sort out an issue you are having with a K3, or is it hypothetical from reading forum comments about K3 issues?
If the former I'm sure there is plenty of advice on offer here to resolve that. If it is hypothetical then don't worry, it isn't an issue, the K3 is one of the best cameras out there at present. Jpegs straight out of the camera should be just fine without the need for any processing.
I'd be surprised to see an image that needed any moire getting rid of, I haven't yet.
I've not used a Mac for processing images so can't fully help you with regards to the best program, but on a budget Photoshop Elements works fine and I'd be surprised if there aren't some free alternatives as there are for the PC.

If you want full frame then with Pentax you are out of luck as Pentax haven't released one yet (other than film 35mm.)
We're forever hopeful for a digital but nothing confirmed to date.

The printing company should change to DPI themselves to match the output size to the image size. whether its 72dpi,300dpi or 3200dpi is irrelevant.
If you want, say, 10x8 inch print from a 5000 x 4000 pixel image, and the printer prints at 300dpi the printers would need to reduce the image to 3000 x 2400 pixels. It doesn't matter what the original resolution was, it doesn't enter the calculation!

That image will take some sharpening with the 'unsharp mask' such as in Photoshop Elements. If you used the converter you will find it will reduce the optical quality of the lens and will have doubled the focal length making the depth of field is very narrow. Closing further to f11 will increase that (but go too far and diffraction reduces sharpness.)
Teleconverters generally work best with longer telephoto lenses to get some extra reach.