The basic questions are these:
1) what upgrades do we want to build per week (prioritized)
2) what is those most efficient way to build those upgrades (in influence cost and queuing - not keying mind you)
3) how much influence can we reasonably accrue per week to pay for these?
4) in the likely event that our wants exceed our influence income, how do we want to increase income and reduce costs?

I generally can't sleep when my mind is chewing on a problem, so I started constructing a spreadsheet to allow assessing the answers to these questions.  At this point, I have looked at 1 (based on Fuzzy's description of what upgrades we do now and what ones we'd like to have), and have a decent sense of how to answer question 2.  I have some data on #3 but haven't analyzed it yet, and 4 can't be answered until after that.

In the interest of getting some sleep tonight (unlike Amanda, I like to sleep more than 4 hours), I'll share just a few I have discovered, and a quite possibly confusing spreadsheet that is a work in progress.

* we have 336 free "build hours" per week
This is highly relevant, because it costs TEN TIMES the base upgrade cost to build it instantly (for a total influence cost of 11x the base cost).  Effectively, by waiting you are getting a 90% discount on the purchase price.  But there are only 336 hours of waiting in one week to have (7 days * 24 hours/day * 2 queue slots).  If the stuff you want to build in one week takes longer to build than that, you will be insta-buying.

* 2x guild missions per week (w/o trek) takes 168, 216 with trek
* MF and gold bonus continuously takes 252
Add these together and we can already see things have to be sped up
* continuous karma takes all 336 on its own

Once you know things need to be sped up, how do you decide which ones to speed up and which ones to wait through?
* turns out to be easy: don't speed up the ones that have the highest influence to build time ratio
practically speaking:
* never EVER speed up the guild world event boss
* from there, don't speed up guild bounty, gathering bonus, 10% magic find, and 5% gold (karma is the next one after that, which can't help but to be sped up)

If you are going to speed up anything that costs more than 200 influence, buying an asura contract lab makes sense (it costs 200; 220 to speed up; while a 500 influence item costs 5500 when sped up - so a net savings of 5500 - (2200 + 500) or 2800 (basically a 50% off sale).

* Speeding stuff up is expensive; keeping karma up for example would take 38500 influence per week, gold is 23100, gathering 19250.  So make sure it is worth it, especially if we are considering using gold to buy influence.

* Influence bonus upgrades look crappy for all but the largest influence generating guilds, it takes ~20000 influence per day to break even on them if you have to speed them up.  If you actually waited them out maybe they make sense, but we never would unless we turned off a lot of other things.