Nice looking Spencer. If you would look near the back of the saddle ring bar and if there is a US inspectors cartouche similar to the one below. You might have to look close as there sometime stamped lightly. Below are the serial # in the range of your which is not listed. You can't read anything into these number as if its not listed it not listed. These were issued late in the war so the condition reflects that.
3309760C 65CO F 19TH NY VOL CAV
3324860C 65CO F 19TH NY VOL CAV
3330560C 09 64CO E 19TH NY VOL CAV
3344560C 03 65CO L 2ND NY VOL CAV
3344860C 09 64CO E 19TH NY VOL CAV
3347460C 65CO M 2ND NY VOL CAV
3347860C 65CO F 19TH NY VOL CAV
3350060C 06 65CO I 3RD MICH VOL CAV
3361260C 64CO I 3RD MICH VOL CAV
3361260C 06 65CO I 3RD MICH VOL CAV
3361260C 06 65CO I 3RD MICH VOL CAV
3364760C 061065CO H 6TH NY VOL CAV
3379560C 65CO M 2ND NY VOL CAV
3380360C 65CO M 2ND NY VOL CAV
3388160C 03 65CO L 2ND NY VOL CAV
3388660C 65CO M 2ND NY VOL CAV
3390560C 02 65CO D 1ST VT VOL CAV