Compression of a pulse requires bandwidth, which is absent in continous, narrow band lasers. The one millisecond pulses will thus not be compressible unless additional bandwidth is generated.
If I understand your situation correctly, additional bandwidth will reduce the toal energy available significantly.
Chirped pulse amplification involves two steps: stretching a weak, ultrafast pulse over space and time so that the amplifier does not burn out, and then compressing the amplified bits. Successful compression requires phase matching in order to obtain a single output pulse.
Also see here.
Note: Fifteen terawatt picosecond CO2 laser system, OSA Publishing > Optics Express > Volume 18 > Issue 17 > Page 17865, describes a CO2 laser system providing ultrafast pulses with very high power levels. This is a MOPA system. Open access: (http://dx.doi.org/10.1364/OE.18.017865)