Pilot reported a near miss with another aircraft on final approach which was practicing a simulated instrument missed approach procedure during a training flight at a non-towered airport. The pilot maneuvered away from the other aircraft then proceeded to land.

Narrative

I would like to report a near mid-air collision at Longmont Airport (LMO). With the volume of traffic at LMO increasing due to flight training; there has been a corresponding increase of near misses due to non-standard pattern entries that needs to be addressed before a fatal accident occurs. At XA:34 in the morning of Day 0; a Aircraft X and Aircraft Y came within what I estimate to be less than 200 feet of a collision; at around 500ft AGL about 1 mile southeast of Runway 29 at LMO. I was the pilot of the Aircraft X; on a personal flight with passengers. From my understanding; the pilot of Aircraft Y was a private pilot working on their instrument rating with a CFI on board. It was a brilliantly sunny and clear VFR morning with calm winds; and Runway 29 was in use at Longmont. There were two other airplanes already in the pattern practicing takeoffs and landings. As I approached the airport from the southwest; I made radio calls at 10 miles out; 5 miles out; and then again upon entering midfield left downwind on a 45-degree angle for 29. I entered downwind behind another airplane that had announced they would be departing from downwind to the southeast. The pilot of the Aircraft Y involved in the near miss was approaching from the south and made radio calls at 6 miles out and then 3 miles out. They announced a 'circle to land' approach and stated they would 'probably cut off our approach prior to getting to the field'. They proceeded to fly underneath the traffic departing from the downwind; and enter the pattern in a low left base for 29. As I was nearing my base turn it became apparent that Aircraft Y had not broken off their approach; and were instead flying directly into the pattern in close proximity to both myself and the departing traffic. I did not have visual contact on the incoming traffic due to the sun glare. I was unaware of what they were doing; but assumed they would break off (as broadcasted) rather than fly directly into established traffic. I was already established in the pattern and had the other established traffic in front of me departing to the southeast. As the traffic warning sounded due to Aircraft Y approaching from the south; I assumed the safest and most predictable maneuver for me to avoid the traffic would be to start my base turn. I was unable to announce the turn due to chatter on the radio. Immediately after initiating the turn it became evident that the Aircraft Y was directly below me and still continuing their approach into the base leg. I took evasive maneuver with a quick climbing right turn and asked their intentions. Aircraft Y replied that they were now breaking off their approach and heading to the east. At this point I made visual contact with Aircraft Y in close proximity ahead and to the left of me. I was at this point able to maintain visual separation with a descending left turn; and proceeded to land on Runway 29. ADS-B data indicates that Aircraft Y was directly below me and within 200ft of me in the base turn. Given that Aircraft Y is a high-wing and the Aircraft X is a low-wing; this created a classic 'blind spot' scenario that (in addition to the sun glare) hindered visual separation.I believe there are a few important takeaways from this event; and hope they can be used to improve safety in the pattern at LMO and other non-towered airports that are becoming more saturated with flight training. 1.) Standard pattern entries should be used when there is already VFR traffic in the pattern. It is my belief that a root cause of this incident was an overly rigid commitment of Aircraft Y pilot to complete their approach procedure and fly a missed approach for practice purposes. However; the desire to complete a practice approach should not overwhelm the need to maintain safe separation from other aircraft that are established in the pattern. When a downwind leg has two airplanes already established in it; it is unsafe to continue a practice instrument approach directly through the traffic; into a base leg; and then climb out beneath landing traffic. 2.) When confusing or unclear intentions are broadcast by an aircraft in or entering the pattern; other aircraft should ask for clarification. I think the main thing I could have done differently in this situation is to ask Aircraft Y to clarify what their intentions were. I simply did not contemplate that they would actually try to enter a left base underneath two airplanes that were already on the downwind. In the future; I need to be more aware of any possibility; and ask for aircraft to clarify their intentions when it appears they may be doing something unusual or unexpected. If I had understood their intentions; I could have taken earlier evasive action and/or delayed my turn to base. 3.) I believe the Aircraft Y pilot may have underestimated the speed of Aircraft X in downwind. Recommended speed at midfield downwind in the Aircraft X is 135kts; which is significantly higher than that for Aircraft Y. The Aircraft Y pilot may have thought they had more time to complete their procedure than was actually available. Pilots need to be aware of different aircraft types and allow an additional safety margin for different aircraft speeds.4.) Non-standard pattern entries and other unsafe practices (such as midfield overflights during parachute ops) are becoming more common at LMO. There is an increasing amount of flight training traffic coming from BJC to the south; and traffic conflicts are becoming more frequent as a result (I have witnessed and heard of several similar incidents within the past year from other pilots flying at LMO). I would encourage the FSDO to increase oversight and enforcement regarding safe traffic pattern procedures at LMO.