In my own opinion, there are 3 options
1. Decline the invitation and create a new profile to re-enter the pool. This would give you enough time to sort out all issues. Personally, I wouldn't go with this option.
2. Accept the invitation and go ahead and submit your application. This is assumed you have the medical summary sheet from designated e-medical agent and you have already completed all the tests recommended by the centre. I believe the medical centre forward your medical result to CIC themselves (weather pass or fail). Your role is prove to CIC you have submitted yourself for all recommended tests, subsequently upload the summary sheet given to you by the medical centre. Personally, this is the option I would explore. Only that your medical status may not get updated on CIC until the sputum test result comes out.
3. Hold on to the invitation and explore ways to accelerate the processing time of the test result . There has to be something you can do hasten the process,e.g fast-track fee, persuasion, etc. If you are risk averse, this might be the way to go.