Like said above - there is no publicly known upgrade policy and op-ups only occurs if Y is oversold and the situation can't be solved through other means.
Other means includes clearing waitlists on paid upgrades, accepting offers on the upgrade auctions, soliciting paid upgrades through mail or text message offers, soliciting VDB/reroute with cash compensation.
The "comfort" section is also usually pretty undersold, so first order of business is to move people to this section. Since all OW emeralds are automatically moved here already at time of ticketing, other OW statuses may very well be first in line for this kind of "op-up".
As for real op-ups I've personally only ever held a longhaul Y ticket once and I got an op-up for that, so in my case I have a 100% hit rate...
On many occasions I've seen others being op-uped and IME
* op-ups can be extremely random - couples travelling together can be split up when one of them gets an op-up
* there is no sense of "suitable for upgrade". I've seen first-time flyers getting op-uped (brought her own food since she didn't understand you'll get fed onboard). This may indicate that ticket price trumps status and that turning up at the gate looking smart has little benefit.
* there is a difference in handling if op-ups are handled by HQ or by gate. And there is a difference between homebase and outstations. Volunteering at gate may work at some outstations, will most certainly not work at most of them.
* in general, Finnair is a pretty good teamplayer and honours other airlines' statuses very well, which definitely can't be said about all oneWorld airlines (BA and AB, I'm looking at you). No idea if this has any bearing on op-ups though.
My advice would be to make sure e-mail-address and cellphone is in reservation, pay for the comfort seat and to make a bid for a J seat. If all fails, they will still be in "comfort" with slightly better space. If op-ups do come around, pax in comfort may have a better chance. If Y is as oversold as you say, upgrade bids are more likely to be accepted. If bids are not accepted, they still may offer paid upgrades on email/SMS where you need to act quickly.