It sounds like you've got the right pieces, just a little settings problem.
Disclaimer:
From what I gather from the thread, you have software you want to install without using any compliance checking. However, I don't know how a policy behaves when no compliance rules are set. I assume (hope) it will execute once and not again as default behavior for policies without a detection. Absolute worst case is that the policy will run at every instance, see no detection check to stop it from installing, and continue to install again and again. I doubt that's the case but stranger things have happened. Personally, I do like to use detection/applicability checks to verify the install was successful (or whether to install at all) and to perform self-remediation if necessary. It helps with reporting and doesn't interfere with scheduled installs or anything else I've found.
End Disclaimer
Now, managed software delivery steps that have worked for me:
1. Create the software resource completely including install command lines, any detection/applicability checks needed, etc.
2. Create a software delivery policy that includes the software resource, defines appropriate targets for the policy, and sets a policy schedule. Here is where it sounded like the settings were in question.
a. The policy can define one or more delivery schedules. This is where you restrict install times, not the remediation setting. Set the window to only allow installs at night (8PM-6AM or whatever you prefer).
b. Make sure remediation is on. This allows the policy to actually download and run the install.
I believe the policy should go out and download to the machine immediately. (If that isn't the case, it downloads at the first attempt to run the policy.) The install will wait to execute until the time you set in the schedule.
Hope that helps.