I've been told to speed up, at my own cost

Acceleration is one of the most expensive things a site can do: overtime, weekend working, extra gangs, out-of-sequence work that costs twice and produces half. And it is very often demanded informally, a programme review meeting, a warning about delay damages, a request to 'pull it back', with nothing in writing that says who pays.

Whether a request to speed up carries money depends on the contract, on who caused the delay being recovered, and on how and by whom the request was made. Pressure to recover delay that is genuinely your own is your cost. In between sits the common case: you accelerated to recover delay the other side caused, because the alternative was carrying their delay damages. Each runs on the same evidence, who asked for what, when, in what words, and what it cost you to comply.

Capture the request the day it is made, and the argument about who pays can be had on your evidence. Rely on the other side's meeting minutes, and it usually cannot.