and the transition from "on the runway" to "35ft" must be at your first segment performance.
Not quite the case. (Caveat - I don't know your particular aeroplane's numbers so my comment is only generic). In general, the flare from lift off to screen will be associated with an acceleration to V2 (OEI) or, probably, a bit more (AEO). Further, the gear, initially, will be down, and then commences retraction.
So surely that means you must be able to climb at first segment requirement with the runway slope factored in to achieve TODR?
Again, not quite. The TOD calculations will include consideration of slope (see, for instance
https://www.ecfr.gov/cgi-bin/text-id..._1105&rgn=div8 for the current FAR 25 requirements). Clearly, if slope presents a problem, the weight gets reduced in the AFM to suit the aircraft's capabilities.
Do you have to refer to the First Segment with runway slope factored in to calculate an initial TOW, before only then using that weight to calculate TODR,ASDR?
Not at all. Each of the various limits to be considered can be examined in isolation (albeit that some AFM presentations lump multiple limits into the one chart - eg X-D charts), TODR (OEI/AEO) give maximum weights, first (and the other) segments give other weights, and so on for all the other limits to be considered. After boring ourselves silly with a bunch of different calculations, whichever result gives the lowest weight on the day becomes the limiting RTOW figure for that combination of input variables.