Andrew, you've got the idea 
Just set up with sanitized SW and the f/2, set and forget for a week. The old KISS principle is best
Like Sunny, I don't worry about pH
Well buffered SW and the usual culture routine will be sufficient
BTW my culturing perspective is from maintaining phyto to feed to rots and pods to feed to larval fish...it was the fish that were the research subjects 
And yes, to give someone a start up culture it is that nice clean subculture you want to be giving away.
I just use a reasonably clean room away from my cultures for handling the subcultures and the initial 2L flask culture. At work, it was my office, at home my kitchen. stepping up from the 2l to the 5gal carboy is done right on the shelf of my culture set up...no point in lugging around full carboys since the that 2L flask is typically enough to get a strong enough start to overwhelm any likely contaminants.
Your culture set up looks good, though your right about the temp management troubles. Since your bubbling air into the cultures strongly (and the subcultures have the foam stoppers), you'll be fine with fans for good air exchange so long as what is coming in isn't too warm. An AC unit would be ideal for perfect temp control, but might not be needed pending room temps in your house.
Would it be a good idea to begin that 1.5 L culture in a total of one gallon of water and add medium and buffer as needed to maintain logarithmic growth as opposed to a different amount?
Just set up with sanitized SW and the f/2, set and forget for a week. The old KISS principle is best
Are there simple ways to test pH and density that are not overly complicated and worth the risk if done right? Is this overly complicated to even consider? I'm not doing research. I just want to feed this stuff. Maybe handoff to someone that needs a start up, which would be done from my subcultures, right?
Like Sunny, I don't worry about pH
And yes, to give someone a start up culture it is that nice clean subculture you want to be giving away.
What would be an appropriate setup to perform inoculation, sanitization, and transfers?
I just use a reasonably clean room away from my cultures for handling the subcultures and the initial 2L flask culture. At work, it was my office, at home my kitchen. stepping up from the 2l to the 5gal carboy is done right on the shelf of my culture set up...no point in lugging around full carboys since the that 2L flask is typically enough to get a strong enough start to overwhelm any likely contaminants.
Your culture set up looks good, though your right about the temp management troubles. Since your bubbling air into the cultures strongly (and the subcultures have the foam stoppers), you'll be fine with fans for good air exchange so long as what is coming in isn't too warm. An AC unit would be ideal for perfect temp control, but might not be needed pending room temps in your house.