Tilt live reload for capz-controller-manager is broken

[nojnhuh]

/kind bug

What steps did you take and what happened:
Tilt's live reloading no longer works for capz-controller-manager since #3399. When a relevant file is changed, Tilt instead hangs at these logs trying to update capz-controller-manager while the old version still continues to run:

Will copy 1 file(s) to container: [capz-controller-manager-c97b7db77-cqqg9/manager]
- '/home/jon/github/capz/.tiltbuild/manager' --> '/manager'
tar: can't remove old file manager: Permission denied

What did you expect to happen:
Live reload works the way it used to.

Anything else you would like to add:
I tried adding --chmod=0777 to each of these but that didn't seem to help:

cluster-api-provider-azure/Tiltfile

Lines 122 to 125 in 7af4c11

	COPY --from=tilt-helper /process.txt .
	COPY --from=tilt-helper /start.sh .
	COPY --from=tilt-helper /restart.sh .
	COPY manager .

Environment:

• cluster-api-provider-azure version:
• Kubernetes version: (use kubectl version):
• OS (e.g. from /etc/os-release):

[nojnhuh]

/assign