BE60 pilot reported a runway excursion occurred upon landing after experiencing an unexpected wind condition and a safe go-around was deemed nearly impossible.

Narrative

Upon preparing for landing at ZZZ; I acquired ATIS information which stated gusty crosswind conditions favoring a small headwind component landing Runway XX. I made a conservative landing assessment which agreed with the Tower decision to select Runway XX rather than [Runway] XY. The rough landing distance assessment resolved for a landing distance less than 3300 ft.; which made Runway XX adequate for landing. Subsequent more precise assessment yielded a landing distance requirement of 2900 ft. - 50 ft. obstacle - with a shorter landing roll requirement. Visual approach was normal. Short final was gusty but advisory onboard wind information indicated wind values crosswind consistent with less than 20 kt. from the right; consistent with ATIS information. On short final I reduced speed to the recommended approach speed of approximately 98 - 96 kt. Touchdown was firm and aerodynamic deceleration commenced in normal order. However; about halfway through the landing roll; the aircraft began to feel like almost being picked up and moved. A corresponding lack of deceleration relative to ground visual reference became suddenly obvious. It even felt as if the back of the airplane was lifting. I made a very quick assessment of airspeed for a potential go-around; but the airspeed indication had fallen below 60 kt.; making a safe go-around nearly impossible. As a result; I elected to maintain control of the aircraft on the ground. While still experiencing a nearly uncontrollable gust which felt like a tailwind gust from the right; I maneuvered the aircraft to avoid hitting any runway lighting or structures; and continued straight ahead. The aircraft decelerated in the grass overrun area of the runway and came to a stop with the two main tires deflating. No other damage was experienced to the runway or the aircraft. I secured the aircraft and waited for assistance.The first observation I can make is about the unexpected wind condition with a gust from the right rear of the aircraft. Had I known of such a component; the favorable runway for landing would have been [Runway] XY. I do not recall ATIS providing northerly wind information; although it may have; I don't recall. The second observation I can make was related to the sudden loss of airspeed. This reminded me of ground proximate windshear. I made a decision to remain on the runway out of fear of not being able to maintain a safe enough airspeed for a successful go-around; especially in a windshear scenario. I made the split-second decision that an overrun at low speed would be preferable to a stall during go-around; which would have far more unfavorable circumstances. The third observation was how the condition changed about halfway down the runway. While experiencing a headwind on short final; the wind condition halfway down the runway was something totally different; and the slower the aircraft airspeed; the lesser ability to control the aircraft I had. I do recall applying adequate cross controls; which at some moments during this incident were simply not enough even at full deflection. In the end; I am grateful this resulted only in a runway overrun. I will certainly build a higher margin in the future or avoid the windy area altogether.