How to find a new Body Corporate Manager

A year ago I purchased a 2 bedroom apartment in an inner city apartment in Melbourne. The apartment block is low rise (3 floors) and consists of 27 apartments and is only 5 years old.

My body corporate fees are $1600p/a, which i feel is quite steep for a building that doesn't have gym/pool/onsite manager. It really is a low maintenance building. No grassed area either.

We are  five months overdue for the next body corporate meeting and can't seem to get eta for the next one. Our current manager barely responds to owners emails or phone calls regarding issues.  It's not uncommon for us to wait up to four weeks for a response.
A number of us owner residents have banded together and agreed that we would like to find a new body corp service. We have done extensive internet research but don't know how to determine what is a good choice. Any ideas and/or advice?

Some of the ongoing issues we have had to deal with over the past 12months are:

* The only lift in the building breaks down every few weeks. This is mainly due to the high volume of students that are constantly moving in and out of the building. Luckily I have the direct number to the service desk and they send someone out to fix the issue within 12hrs.
* The cleanliness of the building is near non existent. We are supposed to have a caretaker come twice a week. It's been close to three weeks since the foyer was cleaned and even longer since the carpeted areas were done.
*The undercover garage has two points of entry and exit. The roller door mainly used for entry has been broken for 2months.  This leaves the sliding gate as the only point of access. Unfortunately this resulted in me damaging my car last week whilst I had to back up and let someone else enter the garage. All owners recently paid an extra $190 to have security cameras installed in the car park to minimise vandalism to these doors/gates.
*Rubbish bins are taken out on Thursday nights and will sit outside until the Monday, Tuesday which results in residents having to leave their trash on the ground in the place where bins sit. Stray cats and mice have been seen rifling through the trash.

As you can see, these are pressing issues that require immediate attention and we are fed up with the unresponsive body corp manager.
Am I allowed to name and shame the body corp service here, or is that in poor taste?

Any advice is greatly appreciated.
Many thanks in advance.