On my occasional trips to London, I would purchase a one week Zone 1/2
Travelcard, slip it in with my LT Photocard and be covered for most of my
transportation needs.

With the advent of Oyster, I'm not sure that's the preferred way, or even
possible anymore. Assuming I would need to be in London once a year or so,
what
would be the best ticketing solution these days?

For your next trip you can buy a weekly zone 1&2 ticket charged to Oyster
online and have it sent to your home address. Photocards are no longer
required. https://sales.oystercard.com/oyster/lul/entry.do

There is also a PAYG option which you can also set up in advance over the
website and (if you want) it can take money from your credit card 'auto
top-up' as needed. The PAYG option will 'cap' your travel costs at a daily
rate (which is 50p below the daily travelcard rate).

PAYG might work out cheaper (especially if you do not stay the full 7 days)
but does not work on most National Rail in Z1&2 so if you plan to use those
services, stick to the weekly.