It depends which city you are in. You can get a 5 year license with an elite or DTV in Chiang Mai for example. Technically you are only supposed to get it with a non immigrant visa but seems that every DLT can make up their own rules.
Last year I was on a Thai language course ED visa and left the country for a week with a re-entry permit. My school gave me a letter confirming my enrollment details and a copy of the school's business licence, etc. I was told to keep these documents with me in case I was questioned by immigration. I was never asked anything by immigration when I returned, probably because I flew directly to Chiang Mai which was less strict than Bangkok at the time. My school told me most of the students that ran into problems with re-entry happened in Bangkok.
It's best to avoid leaving the country but if you really need to do it then try to make your trip as short as possible and talk to your school about the possible risks and how to best proceed. You may want to hire one of those agents offering fast track entry if you are worried about the risk.
Visa exempt entry is not affected by the rule change but hasn't it always been a requirement to have 20,000 THB in cash when entering on a visa exemption? People are rarely asked to show it unless the IO is looking for a reason to deny entry but this has always been the requirement as far as I know.
DTV is a 5 year visa with 180 days per entry. Elite is a 5-20 year visa with 1 year per entry (or 90 days per entry for the old lifetime elite that some people still have). Last year I had a 90 day ED visa and was able to open multiple bank accounts without any problem. The length of the visa and/or entry stamp has nothing to do with it. I think the DTV is just too new and the banks haven't updated their policies yet. Now is also a bad time because the banks are under pressure to crack down on mule accounts used by scam call centers, etc.
If you do your 90 day report early (can be done 2 weeks early) then it's possible that you will have to do a second 90 day report before your 180 days is up. The second 90 day report is due 90 days after your first 90 day report.
I have a Canadian APEC card which does not come with any visa privileges because Canadian is only a provisional member of APEC. My card doesn't have any countries written on the back. I can only use it for fast track immigration. It works for fast track immigration at all airports in Thailand and can be used with any visa or visa exempt entry.
You should have no problem to use your DTV to enter while using your APEC card for fast track. You normally show the card to a security guard to get in the special lane anyway, not to the immigration officer (unless you are using the card as your visa to enter Thailand). If you do present your APEC card to the immigration officer then make sure you also present your DTV visa and make it clear you are using it.