Best Cartridge you have heard on a Denon DP62-L turntable

I've never seen your TT but it looks like a winner. A straight fixed arm and an S arm with removable head-shell, that's a great combo.

Do you have a budget?

I have always liked Audio Technica Cartridges sound, and specs, especially wide channel separation and tight channel balance, the combo that presents excellent imaging

For Moving Magnet I recommend:

AT VM750SH, Shibata Stylus, separation 30db; balance 1.0db, $449.

For Moving Coil, I recommend:

ATPTG/2, separation 30 db; balance 0.5db, $599.

I have the AT540 and have always thought it to be a little bright sounding with my rigs. I haven't tried it on my Denon DP62-L yet. 

The table came with a vintage Empire 999VE/X on the straight arm that sounds great but  doesn't want to stay in the groove. Tracks light at .5 to 1.5 grams stylus force. I installed my Nagaoka MP200 on the s head shell and it sounds very good.

I also have a Stanton 680 series with an aftermarket vivid line stylus that sounds very good as well

I am considering moving to a Moving Coil but need to keep the price under $1000 (preferably less) since I will need to upgrade my phono amp.

Back in the late 70’s my local audio store used the Denon 103 mc cartridge on a TOTL Denon TT with the DA-307 arm. Step up device was a clone of the Levinson JC-1 head amp. Despite the conical (gasp!) stylus LP playback sounded phenomenally good! I tried a Grado Signature Two ($500) in place of the DL103. No contest! Despite the overall smoothness and sense of ease of the Grado the 103 ($160) had better detail retrieval and liveliness in comparison.

That experience decades ago with the DL103 is why I continue to use it and keep several versions in my cartridge stable, including a rare gold-body 50th Anniversary model and the 103D with elliptical stylus. It just does well what a cartridge is supposed to do! 

I am suspecting that a slight adjustment of anti-skate would help the Empire do it's job. 

hudson hifi alignment LP, other side blank for Anti-Skate adjustment

Anti-Skate to ZERO, set tracking force. Last: anti-skate.

I spin the platter by hand, lower the arm, see inward skate, adjust to remove inward skate. Check it a bit in from the outer edge and a bit out from the paper label, make the best compromise.