Unless you get really lucky then custom hay operators will not even bother fooling with you unless they just happen to live in close proximity to you. Heck in my area, most custom operators will not return your calls unless you have more than 10 acres.
2-3 acres is simply not worth the investment of transporting equipment to your location even if you offered to give them 100% of the hay. On most small parcels that a custom operator will bother with even fooling with they will want ast least 2/3 of the hay and leave you 1/3, but 3/4 to 1/4 is even more likely on your small acreage if you get lucky. If you insist on a 50 50 split then I can guarantee that you will get zero calls - a 50 to 50 split is sorta the standard for large acreage though.
Since it sounds like you want to use the hay for yourself, then explore putting up the hay loose. Yes it does take up more room to store loose hay in a barn , but it has been done that way for centuries. Balers are only a product of the last 75 years or so and really only necessary if you intend to sell hay. Eliminating the baler saves considerable expense - and headaches.
In all practicality 2 to 3 acres could be done with a hand scythe for cutting, some type of $150 dollar antique steel wheel hay rake, and a pitchfork using either a pick-up truck or a flatbead trailer to transport the hay. If you have a bushog or rotary cutter then use that instead of the hand scythe to cut with. Since you have a loader for the tractor it would also be easy to build a hay loader to eliminate the pitchfork - again videos are on youtube. You can even turn the hay by hand too with a hand rake -videos on youtube on how to do it. Heck if you have no barn space to store the loose hay then it is also possible to shock the hay for outside storage which has been done for centuries too. Shocked hay stores outside very similar to how round bales can be stored outside. Goats are not picky like horses are so there are no mold type worries with them in regards to hay stored outside.
That said I hay with a 26 PTO horsepower Kubota
L285 tractor, using a bushog to cut (yes bushog leaves 30% or more behind in the field in yield loss but as mentioned in other posts a bushog requires almost zero maintenance and is useful for other jobs too), two antique John Deere hay rakes on steel that I have refurb'd, and a small vintage New Holland 65 compact baler. I sell my hay, but I have yet to turn an actual profit as haying on small acreage is simply not profitable and I have a very minimal investment in all my equipment - less than scrap iron value of each piece (excluding tractor which I already had just like you do).
I am doing 4-6 acres or so every year and have yet to turn a profit, but it can be fun if like to tinker with old worn out junk. If you do NOT like to tinker with worn out junk then do not pursue a full lineup of haying equipment as even using minimal cost junk is not cost effective on really small acreage, but it can be fun as a hobby if profit is not an utmost consideration. Pics of my hobby operation have been posted on this site before if you care to search. Last words I will leave you with is to just remember that there is no easy money in hay. Lots of newbies think that it is as simple as sitting on the tractor, but there is much more time and expense involved than that - not to mention physical labor.