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It is possible. You can reach up around the column, push in the release and pull out cable behind dash. It is a bit of work, but it can be done. I laid on my back btwn the seat and pedals and could reach up in behind. Good luck and watch your back.
I'll add ... remove driver seat ... just a few bolts ... gives you loads more wiggle room & kinder to your aching back ... heck you might find "lost treasure". Also, roadsters have additional bracing beneath dash & that's just more stuff in the way. If you're replacing core only, it has an OE ferrule crimped to gage end of core ... thus core can be pulled/inserted only at gage end. Also, suggest loosen (don't drop) column & loosen driver's gage cluster ... replace all those small lite bulbs while you're in there & that'll also help facilitate the cable change. Pay close attention you don't leave any vacuum lines / wires knocked loose. Got bandaids & a stiff drink?
FYI, both my 71 used Wagner p/n 168 bulbs in cluster. They're clear colorless push-in bayonet. I don't recall how many, but last time I got a box of 10 from local parts store & used most of em.
It is a roadster, and I do have the seat out. You are dead on, it's crowded and tight under the dash. When I first put my hand up in their it was very tight, now I seem to have more room for some reason. I suspect I accidentally disconnected something so I will have to check it closely. I am using my wife's compact makeup mirror to see around in their, it's a merle norman 3 1/2" round, works perfect. All my lights are working at the moment so I will probably leave well enough alone for now.
This summer I will need to take the gage section out to fix/replace the oil line to the oil pressure gage, it isn't working at the moment. Hopefully the line is just plugged up.