Knowing what model tractor the hoe is attached to may help searching salvage yards, then hopefully they will list what hoe is mounted on it. I have found it easier on older equipment to use the OEM part number for the specific part you're looking for.
Messick's has a complete parts diagram for the 723 backhoe. Here is a link to it:
New Holland 723-SERIES - FORD BACKHOES(01/61 - 12/65) Parts Diagrams If you scroll clear to the bottom (hopefully it still shows it when you open it) the part number for the complete cylinder assy.
What I'm seeing is quite possibly the P/N for the cylinder you're looking for being Part #
192316. I ran that number on Google search and found a used one, but it is sold, but does list the price:
E1NNB579AB | Ford 555 Hydraulic Cylinder for Sale Used price listed is $600.
Seeing that that swing cylinder came off a 555 TLB, I ran a search through TractorHouse for a 555 TLB and got quite a few results, 12 to be exact:
E1NNB579AB | Ford 555 Hydraulic Cylinder for Sale Whether those are 723 hoes mounted on them would have to be confirmed through the salvage yards.
But looking at the price for a used/as is condition cylinder that will probably need rebuilt and possibly in no better shape than what you already have the $600-$700 price to rebuild what you have doesn't look so bad. That is the chance you take buying used when you cannot see the internals. The hydraulic shop should rebuild it to like new condition with a 90 day warranty. I had the left bucket cylinder rebuilt on my Case 480C 12 years ago with the same warranty by a local shop. No problems as of yet.
Last year the right cylinder started leaking and decided to put a new seal kit in it myself. A PO had been into it and had tightened the gland nut so tight I could get it out. I took it to another hydraulic shop, since I have moved further away from the shop I had the other one rebuilt at. They had a time of it getting it apart but got it. They called me and said the rod needed re-chromed. And yes, I did notice streaks on the rod from wear, so told them to go ahead. That cylinder cost me right at $580 to have rebuilt but is like new and should last me a lifetime. Cost was mostly labor getting the thing apart. Re-chrome was only a few $$ over $200, which really surprised me. Seal kit was around $90. I know you can buy aftermarket kits for less, but shop I'm sure had to add 30% to cover shipping and for profit.
AVSPARE shows they supposedly have one/some NOS one's in stock, but wouldn't be surprised if the price starts around $1500 and up:
Cylinder Swing, 10', 3-1/2" x 12-5/8", 7/8"-14 Port, for service use P/N 198368, See Group 2-1A, 192316 192316 - New.Holland | AVSpare.com
All that to say that's probably not a bad price for having yours rebuilt, when you look at the price of used parts and basically buying a pig in a poke. You just have to decide what it is worth to you to have it repaired properly, "properly" is the key word here.