Remove direct bitcoin calls from qt/clientmodel.cpp

Summary:
Partial backport of Core PR 10244
https://github.com/bitcoin/bitcoin/pull/10244/commits/fe6f27e6ea68a139d3a98b30a53706008ef8b132
Progress towards T417
Depends on D2817

Test Plan:
make check
ninja
bitcoin-qt # sanity checking; check traffic graph

Reviewers: deadalnix, Fabien, #bitcoin_abc

Reviewed By: deadalnix, Fabien, #bitcoin_abc

Differential Revision: https://reviews.bitcoinabc.org/D2818