So there were really two separate but related issues:
1. My denied application for the Explorer card and the incorrect information I was given by a CSR on the reconsideration line
2. UAL miles expiring 03/31

And here's what happened:
1. The biggest issue was the incorrect information I received from a CSR on the reconsideration line. I followed her instructions, but because she gave me incorrect information, my second call was past the 30 day window. So Chase would not reconsider my original application despite me escalating the call two levels of supervisors. I had to do a new application (which means another credit pull which I was trying to avoid). After the second application I again had to call the reconsideration line and after about 20 minutes of talking and holding and talking and holding, I was approved. I requested the card be expedited which they did and I will receive it on Monday (03/19).
2. Thanks to help from the FT community I took (and will take) these steps to keep my miles from expiring:

• On 03/09 my son purchased an iTunes album and on 03/14 I purchased a magazine subscription, both through the MileagePlus shopping portal. Both of those transactions have posted in my MileagePlus Shopping Account, but their Status is "Pending," so they have not posted yet to my MileagePlus account.
• When I get my Explorer card on Monday I will immediately use it which means the 50K bonus will kick in, but it may be too late to post to my MileagePlus account by 03/31.
• If none of the above post by 03/26 I will transfer 1K miles from my UR account. Is that enough time for them to post to my MileagePlus account and save my miles?

Thanks again for all your help!