"We are there to dance."
This is your problem. People there to have fun, whatever it means for them.
And if they have the option to maximize their fun/pleasure by selecting partners, some of them will do that.
To build a community which is more concentrated on dancing itself, instead of solving other goals, the option of selecting partners has to be removed or restricted.
However it might be not so productive for the host to do so, so another option is to separate events by time or place or by a sign. Make events where the option to select is open, and one where the option is removed or restricted.
You should expect that any methods of separation which leads to restricting of the choosing part of the event will lead to less attractive partners and less skilled partners when you start with a general public. (there are other possibilities in special cases)
If you seek a solution for you personally - you have only one option - make yourself more attractive, and that the only option which does not require changing the rules or cooperation.
Options like separate events by time or by place are simple.
By time - you have a different set of rules - this day female select males, this day males select females, this day males select males, this day attack-helicopters just fly free.
By place - this corner for attack helicopters, this corner for no offers, this corner accept any offer, this corner plz plz any offer.
This one a little bit more interesting, it doesn't require cooperation with the host(besides them not trying actively interrupt such cooperation) but it requires to cooperation with those who think like you.
You have a token, which you can visually identify.
And those tokens could be given on entering the event, if host cooperates with you, which makes things easier but not a necessity.
You choose a token and the rules. A person which agrees with those rules, have a sign of the agreement by having the token visible. By selecting different tokens you can make the task of hiding them harder or easier.
If you have just right now an idea to make tattoo on a forehead, slow your horses, the ability to easily hide token might make things more interesting for others for reasons you do not need to know yet, thus making the idea more attractive for others to participate.
The sign itself, might not necessary be a token, it might be obvious action, pose, hand gesture etc. The idea is old like times where dancing was more popular and was only entertaining besides shooting or piercing opponents on a duel. So check history books. Sell handheld fan on entry, with the scheme of different gestures.
Making token and idea more attractive for others will broaden your options, but worst case scenario you will dance with people like you in a crowd of others.
Cheat code one - if the host is in business, select the most attractive token and forbid others to have it, besides those who agreed with rules. it might be a dress or something less expensive. And yes, do not trust yourself to make those rules, you should find other peoples like you and figure the rules with them together, and adjust them if needed, or it will fail.
Cheat code2, bitcoin flavor.
have different tokens, beginners, amateur, a super hero.
You give the beginner token to a beginner which would like to join your event club and give him a number and coins with this number(not necessary, but the initial state should be registered and associated with the person). (pieces of paper, or stickers with printed QR codes) After each dance, you exchange random coin with the partner.
At the end of cycle let's say 10 initial coins, you have given all yours to different people, and got from them those which they gave to you.
You register that cycle, it can be done differently - real tokens, online with a phone app, have a human which keeps track of them etc.
This not allows you to detect those who do not change partners(however it allows to be suspicious about them), but it allows you to clearly(except cheating) to detect those who did change partners more often. You can give those people different perks and bonuses. Keep track and upgrade tokens for members of your system.
Cheating in the system isn't bad it allows less attractive partners to compensate the factor with harder work and using tokens as bargaining chips aka money which measured in dancing work without restricting freedom of choice. However, to it to be useful it requires the ability for both parties to check verify the "money", and numbers with QR codes are good for that.
The system could be developed further, but keep it simple might help to involve the people in the system. Tuning the system itself allows regulating the proportion of people with different intent. But do not forget about perks, it could be special events, where only high ranked people allowed or something like that.
Bonus of such system is that people can select different strategies in it.
You should understand and accept, there are absolutely 0 reasons to minimize my satisfaction to increase your satisfaction if we do not have any relations. Thus speeches are ineffective if they do not impose some ideology.
So another general thing to do is create different relations than these which the current system creates. Creating special club with events besides those dancing events, and other methods which broader/create the relation connections between members of the group might help. It not necessary has to be other events besides dancing, but it could be just feeling of belonging to a group, however, the feeling should have reinforcement by some stimulus or combination of stimulus.