I run conventional oil, shell Rotella T Diesel Oil. Menards has it a at a great price. Has the ZDPH. Others, some of the diesel oils, off road, racing oils still have the ZDPH. I am also one of the guys that made quite a fuss about this.
JeepHammer say kinda a waste to put synthetic in a carbed engine. Our low HP, low rev, carbed engines that are usually rich will contaiminate the oil before the extened change cycle. That makes good sense.
One exception for the synthetic..... If you use the CJ in the Very Cold climates, like MN, the synthetics do not get as thick and may offer more protection.
For the poster above... I would not use the 40w for winter use. Too thick and may pump up the lifters too much and cause some issue and valve trane noise. Saw you were from MN. FYI.
Last... do not use the Frame Oil Filters on the 258, the allow the oil to drain out and have more of a dry start issue. They were also rated poorly for filter quality. Some good articles on both filters and oils if you do search. I found a great buy on Mobil 1 filters a yr ago $4 each and stocked up. Wix and few others were rated better.