My Ruger 77/357 has out shot all but a tc encore, and believe it or not, a handi rifle. The ruger fits all of your criteria as well. It's not the cheapest nor the most expensive, but it is by far and above the the lightest and most pleasant to handle and shoot. As stated by other, you need to mind the load it likes, but when you do, 1" groups at 100 yards are an all day thing. 38's are the same way. And if the clean breaking 4lb trigger is too heavy, volquorsin make a trigger spring to put it under 2lbs. I left mine stock and most people don't mind it because it breaks very clean. I hope this helps.
That was my experience as well with a bullberry 10" 357 max barrel on my contender. Groups were terrible with 200 gr lfn until I tried AA1680 and upped the charges. Then the group tightened right up.
To the OP, I'd suggest a custom rifle or custom barrel on a contender or encore to achieve your goal. Many factory rifles and single shot barrels have chambers that are less than ideal for top accuracy, some have a barrel twist not friendly to heavy bullets and some repeaters won't feed or chamber the heavy bullets when seated for best accuracy.
I prefer the feel of the contender to the encore, you don't need the strength of the encore for the 357 mag nor the weight.
Probably the most accurate .357 (on average) for less than $1000.00 would be an H&R/NEF Handi-Rifle. If Henry adds .357 to their new line of single shots I bet it will be accurate. Bryan Pierce is awfully fond of the Marlin 1894 Cowboy and Miroku made Winchester and Browning 92 but those are $$$.
Currently casting and loading: .32 Auto, .380 Auto, .38 Special, 9X19, .357 Magnum, .257 Roberts, 6.5 Creedmoor, .30 WCF, .308 WCF, .45-70.
Interesting. Eabco is only a few miles from where I live. Will have to check them out.
Many pistol loads are very sensitive to bullet and velocity in order to match the barrel twist. When we had a .357 rifle, DA, SA and single shot pistols each of them liked a different load/bullet combo due to different twists.
BP | Bronze Point | IMR | Improved Military Rifle | PTD | Pointed |
BR | Bench Rest | M | Magnum | RN | Round Nose |
BT | Boat Tail | PL | Power-Lokt | SP | Soft Point |
C | Compressed Charge | PR | Primer | SPCL | Soft Point "Core-Lokt" |
HP | Hollow Point | PSPCL | Pointed Soft Point "Core Lokt" | C.O.L. | Cartridge Overall Length |
PSP | Pointed Soft Point | Spz | Spitzer Point | SBT | Spitzer Boat Tail |
LRN | Lead Round Nose | LWC | Lead Wad Cutter | LSWC | Lead Semi Wad Cutter |
GC | Gas Check |