Ross 294S Shifting Overhaul, Help
You're on the slippery slope of upgrades here - be leery of tipping money into parts for an old bike that might require other replacement parts.
In this case I think you'll be okay, assuming the parts are as-described.
6/7/8 speed cassettes all share the same spacing and cable pull, so if your brifters are really 7 speed, it should work with the drawback of the one extra click.  I suggest you tune it so the missing gear is higher than your top gear (ie, harder than the hardest gear with the smallest-tooth cog at the rear)  This will reduce the chance of you clicking into the ghost gear and sending the chain &quot;over the top&quot; into the wheel by accident.
To clarify - &quot;friction&quot; means that your gear levers can be set in any position, including between gears.  Brifters and indexed shifters have detents and stops and rests so that each click should put the chain in the right place.  Either is fine, some people prefer the &quot;feel&quot; of being able to adjust shifters precisely, others prefer the speed of press-click-change.  Raciers in the last 20 years have not used friction shifters, they were last used in the Tour in the 90s, and often just on the front derailleur.
I think you can do this.  Take your time and work through it. Pick a window when you don't need the bike immediately so if something crops up, you're not under pressure.
Lastly, save your old parts.  Clean them, oil, and dry-store them for some future day.  Decent retro parts are hard to find.