I agree with getting it field ready but I would put it out there at a higher price now and wait for the buyer to find you who is getting ready for Spring hay. Things are seasonal but that doesn't mean they sell the week before they are needed. I am planting corn in the Spring and I am just now completing my equipment additions and getting my field testing done on the old equipment to make sure I will be "plug and play" come Spring.
I have the following balanced head mowers: 115 mid mounted, 120 semi mounted, and 100 trailer mowers. Yours sounds like a 120. I bought my 120 locally on ebay for $107 and it came with a lot of extras, field ready, missing cylinder was replaced with a very large turn buckle. I bought the 100 for about $85 at an auction in working condition but needing minor work. The 115 I bought 100% complete from Rick out in MN and had trucked here. Total cost was somewhere in the $6-800 range. It lives on the SMTA and has worked and been used yearly since it was purchased...great mower. At auctions the past few years I have seen a 120 go for $270 and a beater 100 trailer went over $600. A pile of parts next to the 100, including an untested balanced head, went for over $300. Around here your mower in working condition will realistically sell for $2-300 if listed on Craigslist and you patiently await the right buyer. Anything much higher than that is either random luck or a regional demand based on some particular need. When hay is high, hay equipment goes high. Two years later you won't be able to give it away.