My answer to your questions:
How is having only six skill lots negatively impacting your gameplay experience right now? If you can cite specific examples, even better!
An obvious answer to this question is a lack of variety in something you're intended to use repetitively. Whatever the amount of skills usable is; its the limitation to do something that is always going to be a factor against your entertainment.
A spellcaster class is an example of a class that is more interesting when more options are available.
On the flip side, how would having an extra skill slot improve your game experience?
A new skill slot alone would make the current gaming experience marginally better, and possibly marginally worse for others as a result. You would have a small new variety that wouldn't be interesting enough to notably increase your enjoyment. On the flip side, the new builds as a result might ruin other players enjoyment much like an OP build can when one player is sucking all the fun outta the room by smart bombing your screen.
However in my opinion, a new skill slot designated for a new TYPE of skill would give you the upgrade in game experience you're looking for out of new expansion skills. For example, currently we have the ultimate-esque skills for each class that sort of morph your hero into a class avatar. WotB/Archon/Gloom/Serenity/ ...big bad voodoo?...; a 5th skill could be designated for more skills like that - they have longer cooldowns and also longer active time. It could be multiple types of ultimate abilities too other than a hero morph. Something like a wizard's chromatic orb that has a short cooldown, high damage and powerful random elemental/arcane aoe explosion effects (polymorph/confuse/earth fragment grenade/flurry storms).
Or the 5th skill could be a skill you charge (hold the key down for long time) and if charged long enough and another spell is used during charged release; changes the effects and mechanic of the charged spell.
Example; a barbarian charges before leap (with DFA rune) and leaps onto a mob of enemies about 30yds in diameter and the charged leap rune effect has a larger radius that stuns all the mobs.
Lastly, the 5th skill could be an alternate spec button that you cast to transform your skills/passives into another set.
Again, it probably would be very enjoyable. However, the devs would still have the challenge to offer the right set of abilities that won't unbalance the game from different perspectives. Appears of course nothing like that would/or could be slated for RoS, but you did ask.
If you had a 7th skill slot, what additional spells or abilities would you add to your bar (on top of the builds you use currently)?
I don't really have an answer for that, because I'm not intrigued by the idea. I am sure something would fill the slot and it would be used frequently. I know I'd put leap in any of my barb builds that did not currently have leap.
EDIT: I forgot I had two other suggestions for 5th skill slot