Phono Cart Impedance Question

I have a little bit of hiss through my 6 ohm, 0.28mV cart but only at a volume pushing the upper end of my listening volume...and it's only audible before I drop the needle, and even then not from the listening position.  I realize I therefore likely have a "non problem"!  

But I still have a generic question on to the sensitivity of producing hiss as it relates to cartridge impedance alone.  If one kept all other cart specs identical (including output of course) would you expect hiss to go up or down at the same volume and system gain if I used an 8 ohm or 12 ohm cart instead?  It seems like the hiss would likely go up just like moving to a higher impedance speaker under the same gain setup but perhaps I'm looking at this incorrectly? I realize moving to a slightly output cart could very well reduce the hiss.

Thoughts?   Sorry if this is a ridiculously obvious question and answer.

I realized I had a spare pair of Mullard 12AX7's from a preamp I sold, so I started experimenting a bit this evening.  The long and short of it is that I've ruled a bad/noisy tube as the issue.  I swapped the Mullards into the 1st gain stage - exact same white noise at very high volume when stylus hasn't touched the vinyl; again, the noise goes away once it touches and this volume level is really louder than I'd ever listen.  I then replaced the original tubes into the 1st gain stage and used the Mullards in the 2nd gain stage (which actually increases the gain by 5dB as they're replacing a pair of 12AT7's).  Same exact white noise under same volume conditions, albeit a bit louder just because of the gain.  I then used one of the removed 12AT7's from the 2nd gain stage and swapped the output stage 12AT7.  Again, same result.  I then replaced all tubes back into original configuration - the sonics are actually best that way, unsurprisingly.

So I now suspect this is an RFI issue with the cart/cable relationship.  I see there are no shortage of threads on this forum about RFI and phono.  Again, this really isn't a huge problem and perhaps I should stop obsessing over white noise hiss that only is audible when the volume is cranked with a LOMC cart before the stylus ever touches the vinyl.
I doubt RFI three. All the original tubes in my ARC were noisy. The SLN tubes if I remember correctly are 1 in 100! But it could be just inherent noise in your phono section. It does not seem that bad according to your description. The best thing to do might be nothing rather than spend money chasing your tail. My own rough test for phono noise is if I can hear it between songs over the background noise of the blank groove I'll go after it. If not it won't matter.
@mijostyn  I'm thinking you're right and I do feel like I'm chasing my tail for no good reason.  I think this is likely normal noise in the phono section and perhaps I could lower it slightly buying a set of Roger's super low noise tubes but I'm wondering if the juice is worth the squeeze.  Noise isn't audible from listening position and goes away entirely when needle hits the record.  I suspect anyone with a LOMC and a tube pre will hear some white noise hiss if they crank up the volume before the needle hits the vinyl.
If you are talking levels that are only vaguely audible with ear pressed hard against speaker then I would say I might have the very slightest hiss at about 80% volume.
This is so slight though but I could even be imagining it.
Seated, needle in groove, anything at sane volume level..... Deathly Hallows quiet.

This is with a Chinook tube phono.
Running through a Denon au320 sut prior to it.

I would relax and sit back and enjoy.
Maybe think about the sln tubes at $90 each......
@uberwaltz  Agreed.

What do you guys think...if I wanted to perhaps try just a couple of the SLN tubes to see if they start to lower noise where would be the best place to start?  As follows:

1st gain stage (pair)
2nd gain stage (pair)
output stage (single)

It would be nice to just dip my toe in the water to check for improvement w/o making a financial commitment for all 5 SLN tubes at $95/ea.  Where would the biggest improvement most likely be heard?