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.

@mijostyn   Thanks for the link on tubeaudiostore.  I've never ordered tubes from him but those Super Low Noise tubes sound compelling.  Although super low noise certainly comes at a price!
Thx for that link Mike
I am on the lookout for some more tubes for my Chinook but very wary of eBay sellers and some of their claims.
Will give Roger a trial.
Yes, they are pricey but every last one I have gotten from him has been super quiet, 6 so far. They test each tube individually on a tester I think Roger actually design. Clio works for him. Earth to Clio! Want to chime in?
I did not realise it was "that" Roger ... Lol.
Just had email reply as did not see 6922 sln tubes online but he has them at $90 each.
Times 4.
Ln are $70 a pop.
Wth, it's only money.
You have to pay to play
Yup, that Roger. Hope you like them. They made a big difference in the noise level of my ARC and lower noise means better sound in some respects. They work so well I have not felt the urge to change phono amps ever since I started using Roger Modjeski's (hope I spelled that right) tubes. Go for the SLN tubes. It would cost you a lot more to get a quieter phono amp!