After reading and trying out the rules on the Offer/Telephone markers and finding them not very intuitive we are using them this way in our games and find this rule much more logical.
When you are in an Event ( party, reunion, church meeting, etc.) the only way to meet new friends ( other players ) is if they offer you their telephone number ( you then choose who you will call and establish a relationship). Once you make a new friend and have his/her phone number you can call him ( only once per game) to ask (force) him/her to come with you to another event or try to convince him/her to take you along to an event.
Just a note of clarification: per the original rules the telephone markers are used solely to establish the initial contact with another player. You either play them to force contact or you choose theirs if they offer (forcing their involvement in your activity, unless multiple are offered). After contact has been made, however, you can force them to come with you an unlimited number of times per game. No markers are needed for these future outings, they are solely for initial contact.
This issue was pretty hard to wrap my head around as well, but after reading the rules 1,000x and then finding clarification on BGG from one of the developers himself, this seems to be how they are supposed to operate.
Your variant is nice, however.