To all who have responded, thank you and I do understand the distinction.
It is in fact the ambiguity of language that I'm dealing with here. When the lecturer uses phrases like "the person on the train sees...", they are implying 'after removing the effects of doppler shift' or 'only considering the effects of SR' but they don't say it. Meanwhile I'm caught here visualizing a clock ahead and one behind and it seems contrary to what is being taught. Specifically the lecturer suggested that since both observers see time running slower for the other, and, if the both observers must agree on the time on the "stationary" clock once they are collocated at the end of the trip then somehow the "moving" observer was being magically thrust into seeing the future beforehand merely by being moving. That can't be true. I can do the math, that's not the problem. I am beginning to understand SR conceptually but what I'm trying to do now is to take it from what would REALLY be observed, all in, all effects and to be able to say "ok, this part is doppler so take that out and this part is SR or GR".
Amongst other things I am a pilot. I deal with relativity every time I fly. I need to know how fast I'm going. Okay, relative to what? Well, the ground ideally but I can't do that directly. So I look at the airspeed indicator but it tells me only the indicated airspeed relative to the air. First I have to convert to calibrated airspeed to remove effects of the design of the system and that has to do with the speed of sound and hydrostatic pressure. Then I have to convert that to true airspeed based on atmospheric conditions. Then I have to convert that to ground speed based on what the air mass is doing relative to the ground. Training tells me how to do the math but I still have to build a sense of those relationships in my head in order to make it work while I am flying. An intuitive sense of this much change in power produces this much change in groundspeed.
That's what I'm trying to do with these questions. I do want to know what the relationship is between doppler and SR (or any other effects) during high speed flight as they are all going to happen AND to be able to calculate both. But I needed to know a couple of "absolutes" first and the questions above dealt specifically with the values perceived under specific circumstances not the rates of change of time during the action. SR deals with effects on rates of change but I needed to set the stage BEFORE asking the question of what happens once movement begins in order to understand it better.