You're right. The statement does not involve any new mood. Rather, it's a hodgepodge of already existing tenses and moods that are correctly assembled.
Unlike what's written above, authors like Douglas Adams (A Hitchhiker's Guide to the Galaxy) and Steven Moffat (Dr. Who) have actually farcically coined additional moods and tenses that they use and say are absolutely necessary to describe the onslaught of new and verbally precarious situations brought about by time travel as one's future so often becomes discombobulated in another's past, as everything hypothetical has already been done and put to bed, and as improbability over time becomes entirely probable and even the most unlikely things become all but certain with a time machine.
Here is an example:
You mayan arrivan on-when for any sitting you like without prior late
fore-when reservation because you can book retrospectively, as it
were, when you return to your own time you can have on-book haventa
forewhen presooning returningwenta retrohome.
Here is another example:
When our ship arrivesed at Zaphod Beeblebrox's planet yesterday
afternoon, I did'll be expecteding him to invite us inside for tea,
which I'm so looking foreback to not having had tea in such a very
long time, save for yesterday's aforementioned tea which of course I
did have only yesterday but haven't yet had, so I only did'll haved
it, which would be astonishingly like never having had it at all if
not for Zaphod having lorded it over me all day today about how much I
did'll drink and how horrendous it was'll be when I did'll
accidentally spill the entire pot all over the floor like some
complete and utter numpty.
This TVTropes page has a list of where this has been dealt with in various media, but as far as I can tell, none of them are a serious attempt at laying out the rules.
Regarding "if I were to have played football" and "if I had played football," the difference in subjunctive mood (ignoring tense for now) can be likened to that between "if I played," where "played" represents the past imperfect subjunctive mood, and "if I were to play," where "were" represents the past imperfect subjunctive mood, which difference in mood (again, setting tense aside) is none. Remember, in English, saying "present" and "past" in relation to a subjunctive mood has no particular connection in meaning with present and past time. Terms vary, but what is often called the present subjunctive simply refers to the subjunctive, and the the past subjunctive may be treated just as an alternative irrealis.
Let's talk about tense now. Now that we've surmised no difference in their subjunctive moods, let's look at their respective tenses as the difference between "have played" and "had played" isn't rooted in the hypothetical but in what tense these verbs otherwise express. The former being present perfect and the latter, pluperfect, their nuance is the same as that between present perfect and pluperfect, which is that present perfect speaks to present and/or past and pluperfect is strictly speaking to a past that is further into the past than another past, which point becomes less significant as, due to their subjunctive element, both require a subsequent clause that uses the conditional that is automatically later than what is described in the subjunctive's preceding subordinate clause and due to "would" being used for the conditional in all tenses. In a nutshell, the only difference is "have played" has the possibility of referring to the present in its subsequent "would" clause, while the "would" clause after "had played" can only refer to the past, albeit a past further forward than the condition that predicated it. As such, unless "have played" is actually followed by a clause that speaks to a present consequence rather than a past consequence of the irrealis, then all of the possible differences it may have had with "had played" essentially evaporate to make them synonymous.