I've done a lot of research since initially posting.
1. It isn't an annual contribution, its actually more like a monthly contribution limit.
You divide the annual limit by 12, and for each month out of the year that you are eligible (hold eligible plan) you can contribute 1/12 of the annual limit. This is regardless of your status at time of contribution (say March 2016), and regardless of the other months out of the year.
2. The 'last month rule' you posted about means that if you're eligible on December 1, you are retroactively eligible for whole previous year. (But not the other way around, if you're ineligible December 1, you're still eligible for monthly contribution limit for those months you were eligible.)
If you use that December 1 'last month rule', you much remain eligible until close of following year ('testing period'). However, if you were eligible on December 1, but don't contribute full annual limit, rather you contribute monthly limit for those months you were eligible (including month of December), you are not using the 'last month rule' and don't need to keep to the 'testing period'.
So either you contribute monthly limit for eligible months, or total annual limit (monthly limit x 12) using 'last month rule' etc.
3. Catastrophe plan is actually not eligible!
The criteria for HSA plan eligibility is high deductible and high out of pocket - offhand I think $12,700 out of pocket and like $4,000 deductible. I don't recall why, but as far as I recall the catastrophe plan is ineligible.
In addition, from what I recall the catastrophe plan premiums are not qualified and cannot come off your paycheck, i.e. catastrophe plans are not offered through companies only marketplace.
Therefore, catastrophe plan premium costs 15-50% more that what you actually pay, plus can't use HSA for deductibles (so that costs 15-50% more), plus can't contribute to HSA (in excess of annual expenses to lower tax liability / save) -- and you don't really have insurance!
4. Insurance companies offer specific 'HSA' plans built to be eligible.
5. Oxford uses Optum Bank for their HSAs, and they offer some mutual funds, I think they let you invest the HSA balance above $2000.