Would you be desperate enough to connect? It's a bit wasteful of avios (around 25k) but the cash element should be ok. There seem to be options that might work through BRU/DUS/FRA/ZRH/LIS. You'll have to search online then call to book - the fee might be waivable.

Ideally you'd find a combination of two band 1 flights but I can't find availability there (nothing to LHR from BIO/TLS/LYS/PAR/GVA/NCE).

Direct flights do look busy that day.