Slow speed Architect dispute via house ins co

[Spider104]

Hi Everyone, I am 2 years++ into a construction dispute involving architect. legal protection covered so far. Very strong case. All evidenced/on paper. Trouble is that we only have circa 12k left of legal protection and still yet to get to 'settlement stage'. Solic has sent letter of claim, expert witness reports x 2 in ( very positive- Architect + SE). Going to Barrister for advice but solic said for her to draft court papers. Court not an option for us due to £. We want adjudication asap. The other side haven't had our response to their defence yet. Can we switch from ins co chosen solic to adjudicator- fixed fee- so that we can at least get some resolution ? What does drafting court papers involve?? Thanks Spider104