I would get a real mounted one and drill it into studs it one of those coat hangers that you'll have to tuck your knees to do every rep.
Ultimate Body Press Wall Mount Pull Up Bar with Four Grip Positions https://www.amazon.com/dp/B003TYJMV2/ref=cm_sw_r_cp_apip_6z8yhEwkhqZ3R
Towers can be expensive, try to find one on craiglist.
I do not like them because they feel unstable, it's better to buy a power rack. If you are on a budget, I suggest you something like this http://www.amazon.com/Ultimate-Body-Press-Wall-Mounted/dp/B003TYJMV2/ref=sr_1_8?s=exercise-and-fitness&ie=UTF8&qid=1441879958&sr=1-8&keywords=pull+up+bar
Yeah, rings require a minimum of 2m height, in fact I go to a park and hang them on a 4 m tall structure
wall-mounted pull up bar, put it lower to the floor https://www.amazon.com/Ultimate-Body-Press-Mount-Positions/dp/B003TYJMV2
The door frame ones are suboptimal, the door frame is not meant for that kind of abuse
Have you thought about a wall mount style?
Ultimate Body Press Wall Mount Pull Up Bar with 4 Grip Positions and Upgraded Design for 2019 https://www.amazon.com/dp/B003TYJMV2/ref=cm_sw_r_cp_api_i_XjiCFbBJ3PT35