OP,
The mention of roof tiles in your post #16 seems to be a first mention of the roof previously being off - why was the roof cover off?
1. A double brick wall makes a big difference for making the party wall safe for any purlin work.
2. After grinding out all the pointing to, say, a 30mm depth then re-point in a 3:1 sand & cement mix.
3. Then carefully open up pockets in the brickwork - "holes" or pockets one brick approx 4" deep.
4. Then use bolt-ons. See how rot damaged short ground floor joists are extended into wall pockets.
5. Use one length of timber to extend the purlin, and sister bolt-on timbers either side of the purlin & the extension piece. All three bolt-on pieces then sit in the hole or pocket.
6. Once in the pocket you can, if needed, wedge up the purlin to meet the rafters.
7. During this work the other end of the purlin should be firmly fixed on the other party wall - why not post a pic of the other end of the purlin?