You bring up a number of important factors that influence playoff scoring. I'm not sure whether it would be better to separate the "adjusted PO scoring" part from the "team success" part. For at least the last ~30 years, PO adjusted plus-minus could be estimated as well. Strictly dealing with adjusted PO scoring, I favor a more direct approach:

Adjusted Playoff Scoring
I used actual regular season GPG for each team, weighted by number of PO games played that year, to calculate an Expected PO GPG for that PO season. I used the ratio of Actual PO GPG to Expected PO GPG, and multiplied that by regular season league avg. GPG to calculate a PO equivalent of league GPG, which can then be used to adjust PO data. I have used regular season Assist/Goal ratio, although it would be better to have the actual A/G ratio during each PO season.

What you are talking about is further adjusting for strength of team and strength of opposition. The other factors mostly affect totals rather than per-game metrics (number of games to win series, number of series to win Cup) or may be captured in other variables (% teams that make playoffs affects relative quality of avg. playoff team, but this can be measured by strength of opposition). If we stick to per-game metrics, it allows elimination of these extra variables which mostly/only affect the totals.

Another way of calculating a useful metric is to use regular season PPG to calculate expected playoff PPG, then compare it to actual playoff PPG. One could use raw PPG or adjusted PPG (using adjusted PO points as described above in link), as long as one is consistent in each case. The formula for each season is then (RS PPG) * (PO GP) = Expected PO Points. The Exp. PO Pts. and actual PO points are each summed and Actual/Expected yields a useful ratio. I've calculated such number for ~30 of the best post-expansion players, and the numbers ranged from Gilmour's 102-112% (raw and adjusted, respectively) to the lows of Dionne (65% raw) and Selanne (69% adjusted). I also ran a regression, using % of expected as dependent variable, and estimated team ESGF/GA ratio w/o player (weighted by PO games) for team strength and expected PO PPG for expected performance level as independent variables. I used ESGF/GA "Off" ratio, since it was less dependent on differences in player usage (TOI for special teams) and I had the data readily available for most of the players included. The results for this limited sample were (these are all based on career numbers):

- For each .10 increase in ESGF/GA "Off" ratio, there was a .56% increase in outperformance (actual/expected)

- For each .10 increase in expected PO PPG, there was a 1.2% decrease in outperformance.

The other big factor, which you mentioned, is strength of opposition (strength of PO schedule). This could be measured using a weighted overall metric, such as GF/GA ratio, ESGF/GA ratio or team points of opponents... and/or a weighted defensive metric of opponents (GA/game).

I would like to do/see a separate study based on team strength and opposition strengths, measuring how well a player's teams played in the playoffs. The dependent variable(s) could be PO games won, PO series won, or PO GF/GA ratio. The independent variables could be weighted variables such as team points, opposition points, team GF/GA ratio, opposition GF/GA ratio, etc. Using games won would require use of some version of Pythagorean win formula, while series won would require Pythagorean and some additional probability calculations based on maximum length of series.