The problem lies in how you diode bridge the transformer with a large cap. The % ripple you choose will be inversely affecting the peak surge current when turned on.
Thus a 10% ripple voltage results in a 1000% or 10x surge current, much like an incandescent light bulb but may differ depending on your selection and if you have a series choke to reduce Ipk. It may or may not handle this.
The second problem is the inductance of the transformer may be many Henries and depending on the protection built into Insteon's MOV surge suppressor may exceed the Joules of transient energy when switched off. (1/2LI²) ( you could add a bigger MOV)
These SMD reels of LEDs are rated for automotive voltages, so the power will depend on voltage being 12.0 or 14.2V
If you want max brightness and low flicker use 14.2V with a small battery & charger and switch the DC.
If you want cheap solution use 12.0V from PC PSU's
Check specs on 12V for a ~850W+ PSU from a PC and use the 5V enable line to gnd to switch the load on the PC connector.
I would prefer you use two old 500W PSU and check specs on power avail for 12V only. Some old PSU's require a pre-load on +5V of 5% to turn on.
If you daisy chain 160' (50m or 10 reels) you will have I max track current issues.
Distribute power separately as the current from cascading more than two 5m reels may be excessive for the printed FPC tracks.
I use 16 or 18AWG wire to feed the strings in a loop to reduce current and voltage drop. You can decide how much I max & V drop on distribution you can handle.
I have used 200W transformers before that were pre-installed for 12Vac 8W lamps with a 30A bridge and 10mF successfully for LED power, but I used a electro-mechanical timer AC switch.