Just looking at the Ufopedia, the Sniper ammo is massive. 20x140mm HMG, a round that size and the velocities involved would shred the barrel in no time. I'm assuming that the distance of 90.
A possible updgrade to the sniper rilfe isn't ammo, they are already quite big and beefy. A better idea would be recoil reducers/flash supressor forward facing which has a similar effect, to make it more accurate shoot out to 100, heavier barrel to again increase accuracy shoot out to 110. Trade off with these upgrades is user requires heavy and sniper skill to use. I don't think taking it over 110 would be practicle as it would put the laser weapons out of use.
The possibility of making the weapon out of alien materials to reduce the weight, weapon only requires sniper skill. This might have the effect of reducing the distance to say 100 but gives more TU's.
As for lasers, heavy is a better option for sniper it already has great range. A decent upgrade might be focused optics to further increase range and its ability to pass better through particulate.
I tend to favour hybrids, I would think that the best upgrade for the heavy laser would be after researching the plasma blaster, you would then be presented with the ability to research a new heavy laser based on the plasma principle. This would give you a heavy laser that still shoots to 120 but has increased damage, somewhere around the 85 mark, with a trade off in wave mode only. The weapon would use pre existing alien plasma rifle ammo.