I really admire your wish to crack the Pennine Way this way and you will certainly find this section very challenging. Doing this area as you need to though you will find you're expending a lot of energy and time climbing up onto/descending from the main ridge line. You say you can't carry a rucksack, but if you could persuade someone to do it with you doing the lot in one go over 3 days, and using the two huts that are there at about the 9 and 18 mile point from Byrness to 'overnight' would be a good option, or Forest View at Byrness does packages that include dropping you off/picking up from Cocklawfoot farm. Having said that individual comments are below.
Byrness to Chew Green. Steep climb at the start to get you up onto the top at Byrness Hill, but a good track up to the parking spot at Chew Green. Unless you're particulary keen to walk every part of that route it may be better to park at Chew Green, and walk to Byrness Hill, returning from there so missing the steep climb?
Chew Green to Lamb Hill - 10 miles return approx. As above, easy to park at Chew Green
Carlcroft to Lamb Hill via Mozie Law, Black Braes to Carlcroft. Again, easy to park along that road, though you may be better using the parking area at Blindburn. Be aware though that much of the area around there is part of the Otterburn training area, so may be closed at certain times. The firing schedule is available here
https://www.gov.uk/government/publications/otterburn-firing-times.
After that I'd use Cocklawfoot as your parking area, from there you'll face a climb onto the ridge but could head right to Mozie Law or left to Auchope Cairn.
To tackle the part from Auchope Cairn you could either park in KY or further along the road towards Burnhead, both would allow you to take either the lower or higher route.
Others may have better ideas