Let's crunch some numbers.
In a city run, approximately 100-200 singles fall in an average run. If you're lucky, you might get 1-2 100s. If you can clean out the zone, you can meet or exceed 500 total pieces of currency in a single run.
However, the average for a large Dynamis shell is closer to 200-300 a run. Still pretty sweet.
Most of the relic weapons cost anywhere from 120-150 or so pieces of 100 currency, assuming you can borrow some of the last 30 100s needed for the final 1000 piece. That's 12,000-15,000 singles.
If a single person sponsors a run for a shell, it will take them on average a year to complete a relic. If you rotate sponsorships, then it's closer to 3-4 (the latter scenario is where I am.)
So, I think that people going into such a linkshell with the expectation of funding a relic may be disappointed. It's far more reasonable to have an open sponsorship system for people who want to pay for a glass and potentially make 2-3 million gil in profit. The issues that stem from that, of course, is that only city runs raked in the 200-300 pieces of currency. Northlands are closer to 100 max if no 100s drop. It's still double your money, but not 600% profit like the city runs can be these days.
So you'll have those rotating out sponsorship relucant to sponsor northland runs. I suppose in this case you can charge individual linkshell members a small fee for northlands runs, and just free lot the currency, or whatever.
I'm not saying it's a bad idea altogether. There probably are some folks who want to upgrade but can't get a sponsorship deal with a shell. If they have a ton of outside money already and think that currency is too expensive to completely self fund, this might be an option. I just don't think a relic can be completely funded in such a way. (Relics also require rare/ex items, and a linkshell that can clear Bastok may not necessarily be able to handle attestations in Beaucedine.)
If you guage the interest to be sufficient, I'm going to suggest a Wednesday/Sunday schedule. Mondays are so piled up that there are six linkshells whose times overlap right now.
____________________________FFXI: Catwho on Bismarck. Once again a top bard on the server: Dardaubla 90 on 1/6/2014
FFXIV: Katarh Mest on Lamia - Member of The Swarm and the League of Extraordinary Crafters
I can't understand anyone who skips the cutscenes of a Final Fantasy game. That's like going to Texas and not getting barbecue.