A few points about tele-converters:
1) A 1.4x TC costs you one stop. A 2x TC costs you two stops. So your 70-300 which I think is f/4-5.6 would end up being a f/11 lens with a 2x TC
2) $15 for a TC is not a rip-off
However, consider that a good TC costs $200 - $250 and the Pentax one is over $450 so I would not expect too much
3) Using a TC with a slow consumer lens like the 70-300 can be a challenge. They are designed to work with fast prime lenses and work best with those.
4) As to mounting it makes no difference. I usually mount the TC on the lens first but it does not matter
5) You say the 70-300 has no aperture ring if I understood you correctly. If so this is an additional challenge as there is no way to control the aperture and it will always shoot at smallest aperture. That might be OK for your purpose but it limits what you can do
6) Since there are no electronics in the TC you will need to set the focal length, focus manually and use stop down metering
Bottom line, it is not impossible to use this for your purpose but you have a lot of hurdles to overcome.
Read through this it might help:
https://www.pentaxforums.com/forums/58-troubleshooting-beginner-help/110658-u...x-dslrs-f.html Both the links and the video have important info.