Cisco – How to Block Torrents Using NBAR

You're right, you wouldn't really see the burstiness easily on SNMP. 1GE can send 1.48Mpps, so it takes very very little time to congest the the 45Mbps, which can handle less than 75kpps.

If your ingress is 1GE and egress is 45Mbps, then obviously the congestion point of 45Mbps will need to drop packets. This is normal and expected. If you increase buffers you'll introduce more delay.
1GE takes 0.45ms to send 40 1500B IP frames, which is right now the amount of burst you can handle. However dequeueing them on the 45Mbps already takes 10ms.

If you don't have any acute problem, I would probably not do anything about it. But if some traffic is more eligible for dropping than other, then you should replace FIFO with class-based queueing. Say maybe you want to prioritize so that more ftp is dropped and less voip.
Then it'll also make more sense to add more buffering on the ftp traffic, as it's not really sensitive to delay.

If you want to try your luck with deeper buffers, something like this should suffice:

policy-map WAN-OUT
 class class-default
    fair-queue
    queue-limit 200 packets
!
interface Serial1/0
  service-policy output WAN-OUT

This would cause 50ms buffers on the Serial1 and would allow you to handle up-to 2.25ms burst from single Gige interface.

Your question's pretty broad. There's a lot of different commands you can use to troubleshoot and monitor QoS, so I'll focus on the primary question you have, which is how to reasonably verify your QoS configuration is working and how to read the policy-map interface output.

The only true way to verify that QoS is working is to hook up a traffic generator and monitor your drop rate in various queues. Since that isn't typically feasible, particularly in a production environment, all you can really do is verify that the traffic is being marked and classified properly.

What you're really looking for, when it comes to verifying if your QoS configuration is working, is for the counters in the policy-map interface command to increment.

So, for example, in the output your provided:

Class-map: VOICE (match-any)
  3860628 packets, 1070196895 bytes
  5 minute offered rate 0 bps, drop rate 0 bps
  Match: protocol sip
    97348 packets, 49867304 bytes
    5 minute rate 0 bps
  Match: protocol rtp
    3763280 packets, 1020329591 bytes
    5 minute rate 0 bps
  Match: access-group name NEC-PBX
    0 packets, 0 bytes
    5 minute rate 0 bps
  Priority: 40% (340 kbps), burst bytes 8500, b/w exceed drops: 5

You can see that you're seeing packets under SIP and RTP, but not NEC-PBX. If you know you're getting SIP and RTP traffic across a link, you should see the packet counts increment and that's a reasonable way to know that your configuration is basically working.