C182 pilot reports critical conflict with aircraft in the traffic pattern during a missed approach from the VOR/DME-A to OKV. IMC prevailed above 1200 feet and the published missed approach procedure is not followed.

Narrative

I was with an instructor and an observer on the VOR/DME-A approach to OKV. We were IMC and broke out of the clouds; however; we were going missed; the ceiling was ragged and I was using foggles. Observer called traffic; to the instructor; southeast (to our left) but did not indicate heading. Instructor verified traffic. Observer also called traffic which was headed southeast but did not indicate that this was a second aircraft in the pattern and did not indicate the heading of the second aircraft. As we crossed the runway; instructor looked to our right and saw oncoming traffic final to RWY 14 and took evasive action (60 degree left bank and climbing left turn at max power). In retrospect; I believe that I should have removed foggles and become a third observer while in the airport traffic area; however; we were going missed; so technically I was still in simulated IMC. Instructor should have verified with observer the presence of the second aircraft; as instructor had 4000+ hours and observer had 13+ hours.After taking evasive action at the final phase of the VOR/DME-A approach I called the missed approach to Washington Center and was proceeding direct to LDN VOR. I requested clearance to ZZZ; however; I failed to follow the missed approach procedures; which indicated climbing left turn to 3000 via MRB R-231 to CWINE and hold. ATC asked what my filed altitude was. I indicated 4000. ATC indicated that that was too low for the MEA. ATC instructed a climb to 6000 and stated that a previous controller must have approved direct LDN. After a pause; ATC then asked whether I'd received instruction from the previous controller. I indicated that I'd just avoided a near miss and was proceeding direct LDN. No further conversation about the topic occurred.Even though instructor took control of the aircraft to avoid the near miss; after evasive action was taken; I should have followed the missed approach procedure; rather than continuing onward to the next airport.