C182 Pilot reported an NMAC with a helicopter and unstable approach while attempting a touch and go at a non-towered airport.

Narrative

This situation occurred during the second of a series of planned touch and go practice landings on Runway XX at ZZZ. While on base leg; beginning the turn to about half mile final; I noticed that a helicopter; which had also been doing practice patterns in the helicopter pattern on the south side of the runway; was hovering in place a few feet above the numbers XX. I then began leveling off; adding power; and announced over CTAF that I was going around. The helicopter radioed that it would move from the end of the runway to maneuver over the taxiway to the south side of Runway XX; and it began to move to the south. I acknowledged the helicopter pilot's actions by saying my aircraft call sign and 'thank you' over CTAF; and then began an attempt to salvage the touch and go pattern and landing. I pointed the nose of the plane at the threshold of the runway; reduced power to idle; and added full flaps. I began to notice that the unusually steep descent angle was resulting in an airspeed increase of almost 30 MPH above my normal final approach speed. Additionally; this fast final approach speed; coupled with the helicopter's relatively low takeoff speed; was resulting in a rapid closure rate between my airplane and the helicopter; which by now was executing an upwind leg over the parallel taxiway. It was becoming apparent at that point that the energy inherent in my aircraft's speed and altitude would prevent safe accomplishment of a touch and go; or even a full stop landing. At that point I initiated a go around by adding power and leveling off over the runway. I was still closing rapidly on the helicopter; and now began to encounter significant roll and pitch excursions; which I suspected were due to the helicopter's rotor down wash. I immediately made a 15-20 deg turn to the right (north) to get out of the suspected down wash; which also created additional lateral separation from the helicopter's flight path over the parallel taxiway. This heading resulted in a ground track which crossed over a building complex abutting the airfield; immediately to the north of the airfield boundary. As a result I flew over these buildings at an altitude well below the normally required FAA vertical clearance. I had never intended to do anything other than a touch and go landing on Runway XX; albeit with a relatively short final approach leg; as I have done safely and successfully many dozens of times previously.What really caused the problem [was that] I allowed my impulse; to not allow the Helicopter pilot's politeness to be wasted; to override my initial decision to go around; and attempted to salvage a touch and go landing from an unusual position; in an intentionally tight pattern that offers minimal margin for correcting off-nominal altitude and speed.[To] prevent a recurrence [I should] continue with original decision to go around under these circumstances. Don't allow sense of politeness to interfere in the face of judgement about speed and altitude needed for safe aircraft operation.I should have simply continued with my initial decision to go around; and just say 'thank you'. A pattern with a half mile final offers little margin to correct for off-nominal altitude and airspeed variations; even when full power is only added for a scant few seconds. I should not allow 'politeness' to be an inordinately important decision factor in such situations. I have gained a great amount of appreciation for the need for separation when flying below; behind; and to the side of helicopters taking off from a parallel taxiway. I have a refreshed appreciation for the limited ability to dissipate excess energy (altitude and airspeed) on short final while flying an intentionally tightened practice pattern.