A
61?
Seriously? Does it have any friends that would like to find a new home?
The obverse has a few minor knocks: a scratch through the cotton leaves and cap, a minor divot beneath the hair curls, and a scratch in the hair above the ear. These are consistent with MS-64/64+. The minor, but persistent, chatter in the fields
has to be what led ANACS to call it a 61.
The reverse has one noticeable knock, a gouge on the second right wreath cluster. By itself, this is consistent with MS-65. The chatter in the field between the right wreath and AMERICA and the rubs beneath the eagle's right wing (our visual left) must be the reason for the 61.
It's all about how PCGS/NGC sees the chatter and the reverse rub. There isn't any way those factors detail the coin or drop grade the coin 3-3.5 points.
Here are the questions to kick around before cracking the slab and resubmitting:

How sure are you that the coin makes DMPL on resubmission? It's hard to evaluate that from the pics, but you have the coin in hand. PCGS requires
complete 6" reflectivity on the obverse and reverse for a DMPL designation. (I'm not concerned about the Cameo designation.)

Look at the rub on the reverse through a 10x loupe. Is there evidence of surface scratching? Or is the rub largely superficial?

Look at the field chatter through the 10x. Is there evident pitting, or is that merely a surface disruption?

Is there any possibility that the disruption in luster in the hair above the ear is evidence of circulation? Is there any risk of this one coming back as a slider? (I don't see any corresponding disruption on the reverse.)

Is there a better shot with PCGS than NGC right now?

If the grade comes back MS-62, would you have a decent shot at a CAC sticker?
If these questions don't cause you any concern, what's to lose by resubmitting it? Purely on a technical grade, I think it is MS-64, with a possible 0.5 drop for eye appeal because of the reverse rub and the obverse and reverse field chatter. IMHO, that should net it to MS-63+, with a probable DMPL designation. If the questions do make you pause, leave it in the ANACS slab. On a bourse floor, it would trade well over 61. Any buyer would see what we are seeing, and price it accordingly.
Just some thoughts. Great coin!