Not only conflict of meetings I see some conflict of interest. Make sure to have your contract reviewed by your lawyer before jumping into new job. Most full time job has clause in their contract where one cannot take similar position in another company . You know once ur blacklisted in IT job, life gets hard .
Ethical advise, being a lead system arch I'm assuming ur making very decent money. Leave the other job who needs it :) .

Also consider tax burden .if single and 150 k plus income with 2 jobs , u end up paying huge . Working online paying tax to multiple states might be something to consider about .

Sum up , make sure you wont hurt your full time job by any means . Contract jobs can be replaced easily but for full time, you know how hard it is to get a decent one .