Depends how much you really want to fly regional jets
, but UA's insane routings allow something like LHR-IAD-SAT-ORD-DEN-PHL-SFO-LAX-SEA-HNL, for around 15K miles each way.
It's the backtrack from SAT via ORD and DEN to PHL that makes much of the difference. This is a great source of *A miles if you have the time, energy and patience.
Expertflyer is the best source of this info, using ITA to validate.
As you point out, unlimited transfers are permitted but that implies a stopover of less than 24hrs. But ORD being a hub, you could legitimately stop quite a few times there
Also note that these routes generally apply to all fares (T, V, W, etc), so you don't have to buy up to B unless you have another reason.
Here's a partial listing on the LHR-HNL route ... it goes on for pages !
LON-NYC/EWR/WAS-CLT/PIT/PHL-RIC/ILM/PHF/BGM/BHM/CHO/CHS/GSP/RDU/
ROA/SCE/SWF/SYR/BDL/PVD-WAS-CHI-MYR/DFW/HOU/GCK/HYS/ROC/BWI/BUF/
SYR/ALB/MSP/ALO/BDL/CAK/DAY/GRB/PWM/CWA/MKE/BMI/CHI/RFD/SPI/DTT/
GRR/LAN/MBL/TVC/IND/SDF/BNA/BHM/FLL/MIA/ORL/GSP/PVD/BOS/HPN/CHS/
RDU/CAE/SAV/AMA/SAT/AUW/CID/CLE/CRW/MSN/MLI/IMT/MBS/MEM/FMY/MHT/
AMA/BTV/AOO/AUS/TYS/JAX/LBL/TPA/DSM/ROA/ORF/CMH/FWA/ATW/ICT/OSH/
YTO/PIA/UIN/AZO/SBN/IWD/PBI/MKG/SAT/LEX/CLT/RIC/GSO/CVG/ATL/SJU/
STT/PIT/PHL/ABE/AVP-CHI-DEN-BIL/BZN/MSO/BOI/MKC/SGF/GTF/MSY/COD/
CPR/GCC/JAC/LAR/RKS/SHR/WRL/SGU/SLC/VEL/PHX/TUS/YUM/ASE/CEZ/COS/
DRO/EGE/FNL/GUC/HDN/MTJ/TEX/ABQ/FMN/AMA/AUS/DFW/SAT/BIS/DIK/FAR/
ISN/JMS/BDS/PIR/RAP/BFF/CDR/EAR/LBF/LNK/MCK/OMA/DDC/GCK/ICT/LBL/
OKC/MSP/ALO/CID/DTT/ABQ/YYC/STL/CYS/RIW/CNY/PGA/ALS/DEN/GJT/PUB/
SAF/HOU/DVL/FSD/AIA/GRI/OFK/HYS/TUL/ELP/FYV/XNA/CLT/PIT/PHL-LAS/
RNO/DEN-SEA/FAT/SFO/PSP/LAX-ACV/BFL/PHX/TUS/SLC/BUR/CEC/CIC/CLD/
FAT/IPL/IYK/MOD/MRY/OAK/ONT/OXR/PSP/RDD/SAC/SMF/SAN/SBA/SBP/SJC/
SMX/SNA/VIS-SEA/FAT/SFO/PSP/LAX-SEA-HNL
hth