Thank you, David, for putting me on the spot.

1) Because basic economy fare does not earn PQF (but does earn PQP), you have to choose regular economy on flight search.

2) In general, weekend is typically bad for segment runs because United reduces frequency to some small stations (also, higher fares). But you can still do a four-segment run from LGA. EWR is not a good choice for segment runs because it offers a lot of nonstop options. I do not know the costs of local transportation for EWR vs. LGA.

3) Booking one-way vs. round trip; the latter offers irregular operation protection. The drawback is that it may be more expensive than two one-way tickets if you want to return immediately (United imposed a minimum turnaround time limits a few years ago). I like the options for doing AA-hub-BB-hub-CC-hub-DD (6 segments) on Saturday and the reverse direction on Sunday. This also saves on taxes (911 security taxes for one segment).

4) The lowest fare is probably $180 for 4 segments (LGA-RIC/ORF/ROC). So, you try to beat $45x15 ($700) when constructing the complicated itineraries. If you also need PQP to reach a status, you can book more expensive tickets.

5) You will need two weekends at minimum to complete 15 segments.

If you need other info, please ask.
$523 for 8 segments in a single day.
https://www.google.com/travel/flight...PT0SBggBEAAYAA