That's my repo - it should be easier than all that.
Looks like the breakout (oh how I wish that had come with mine!) simply omits/combines the two VCC and the two Gnd pins into one each.
You likely need to only wire four things: VCC (5V), Gnd, TXD and RXD. That's all. I suspect Set and Reset are already pulled to their appropriate states (Reset should be pulled high internally, and I think Set is internally pulled high too).
Either way, the wiring looks OK to me in terms of pulling things up to 3.3V, though you're going to need to do the same thing for D6 (reset) you're doing for D3 (set).
That said, I'd unplug those two for a moment and let the resistors do the work.
What's wrong here is that I don't see VCC for the PMS7003 going to +5V... I see it going to 3.3V. While that's fine for the pull-ups, the VCC must be 5V as far as I know (otherwise you'll affect the fan speed, and that's part of the measurement pathway - not to mention it might not even power up).
On a Photon, when powered from USB, VIN will supply +5V.
On the Electron I think the only option is VUSB (and that means having a USB supply... I don't think the LiPo won't suffice). Only wire +5V to VCC... never the other pins or pull-ups on the PMS7003!
EDIT: Once you have the power thing sorted, you might have to reverse the TX and RX connections. I don't recall which is which but try what you have first.
EDIT2: and by the way... where did you get these? eBay, AliExpress, somewhere else? Would be good to know.