That first plumber who installed you sink doesn't sound very professional, and he definitely doesn't take pride in his work. The second guy doesn't sound very experienced or interested in the job.
You sound like you are on the right track, keep interviewing contractors until you find one that can explain things to you so that it makes sense to you, and one who will actually meet with you and leave you with a solid sense that they know what they are doing and that they are there to help you (and not themselves to your money).
If you have an unfinished basement, I don't see what the problem is. Maybe I am not seeing the whole picture of your basement. But as far as I can see, a regular gravity drain waste for the new toilet is totally possible, but you will have to add in a cast iron wye fitting below the existing side inlet tee (it has to be cast iron to support the cast iron already in place, but the actual new drain branch can be plastic).
Unless there are walls in the way of where the drain branch needs to go, your only real concerns are going to be drilling through your floor without hitting anything (although I think you said you didn't want to cut up your existing floor?), cutting into your main drain stack without sending chunks of cast iron into your drain system, and venting the new line.