Sorry for late reply - for some reason I missed this question until Eggtastico 'woke it up' today!
The unusual thing with the Wynn Red Card is that there is only the Red Card i.e. there is no tier system of card changing colour or name etcetera as your spend with them goes up the scale. So without the sample emails of your invitations from Wynn mentioned by Eggtastico it's hard for a rival scheme to know where to place you on their scheme.
Other casinos and groups of casinos operate a tier system where it's immediately apparent to a rival casino the sort of status (and therefore spend) that you have and they will often match that status to attract you to them. For example Total Rewards (look at their website but in Vegas covers Rio, Ballys, Harrahs, Paris, Caesars etc) has four tiers or M-Life (Mirage, Aria, Bellagio, Excalibur, MGM, Mandalay etc) also has four tiers plus a special by invitation tier. So if you had, for example, a Total Rewards Seven Stars card (the one on their scheme that offers complimentary rooms) then an M-Life casino would most likely offer you a Platinum card straight away if you asked at the Casino Host desk (rather than just the Players Club desk) .... with the Wynn Red Card plus your emails of regular free room invitations they could do the same for you.
The key thing is that at the Players Club desk they almost never have the authority to do that and will simply issue you with a new card at their lowest tier. So you need to either ask them to call a Casino Host over for you or go direct to the Casino Host offices yourself (often close by anyway).
Another thing to add is that it's not the spend per trip so much as the spend per qualifying period - bit like VS FC! So if you are a local (i.e. Nevada resident) they often make the qualifying period 3 months so points reset 4 times a year. If you are tourist (i.e. non-Nevada resident and especially overseas) the qualifying period is more usually a full year ..... meaning a relatively small spend but more than one trip a year as a tourist does make you interesting and does allow you to climb up to a nicer tier level than a local could achieve (which sounds like you?).
As a regular I'm sure you have already got one but if not do make sure you get a US ITN number issued to you (valid for ever so only need to do it once) so that you don't pay US taxes on any jackpots of $1200 or more that you are lucky enough to win otherwise they will grab 30% off you as they pay it out (you will have no UK tax liability either, bit like on course betting for the horses in the UK).