I'm interested to hear no one's said wedges/hammer. Some of the eucalyptus trees we mill have heaps of tension in them and even while they can be cut through without wedges, for some reason if I have to back out of a cut (ie after the band has taken a dive) there's no way I can do this without wedges in some cuts as the tension can tightly close up the kerf. Even then this only works near the start of a cut if you are half way into a log and the band has taken a serious dive my bands are not coming out and I've had to cut some out with the chainsaw.
In most cases backing out will also pile up sawdust and jam the band in the kerf so I keep a piece of old band on hand to keep the kerf clear of sawdust. The pieces come from when several of my bands have come off the wheels and wrapped themselves around the drive wheels so much so they had to be cut off with and angle grinder. I've managed to recover some pieces of band around 45" long and taken the set off the teeth by flattening the teeth on a piece of steel with a hammer.
The following is pretty specialised but I'm now maintaining two bandsaw mills at the tree loppers yard and this includes sharpening and setting the bands. It's taken some time to get up to speed with this but I am slowly getting better at quick touch ups and resets which is pretty handy.
As for moving slabs and clearing sawdust we have a very useful articulated loader that stays permanently in the yard. It has interchangeable attachments including forks, and open and closed buckets. The forks can lift logs/lumber up to about 1 ton although above about 3/4 ton the load has to be kept close to the ground during tight turns or the loader can tip. It's not as bad as it sounds because with the load near the ground the loader tips until the load touches the ground and doesn't tip any further
I usually park the loader alongside the log being cut and provided they are not too heavy slide the slabs direct onto the loader like this.
Here I was using one of my CSMs
To clear sawdust I swap the forks for the bucket and make a couple of passes long side the mill - the sawdust gets dumped on one of the wood chip piles.
For heavier logs there is a Kubota Tracked loader(with loads of attachments long forks, grapple, various buckets and mowers etc) but while it can lift close to 3 tons this thing is a bit of a brute and has bumped the mill and several times pushed the mill and its tracks off its concrete pad. The Kubota is mainly used to move logs around the yard. I don't have my ticket on this machine but as this is usually out of the yard on other jobs its not available most times in the yard anyway.
Heavy logs are usually lifted onto the mill and turned using a HIAB and chains. if the logs are small enough I rotate them on the mill bed using cant hooks.
The bigger mill is mainly used to make cants small enough to fit onto the smaller mill which is a bit more precise at milling.
BTW my job is not really to mill bulk timber but to maintain the mills and sharpen the bands although I occasionally use the big mill to make cants. I make lots of test cuts on both mills and am able to cut stuff for myself but these last few years I have accumulated so much I cut very little for myself. If the test cuts are of no use to anyone, every now and then I throw some onto the back of my van and take then to a local mens shed (community wood/metal shop) for mainly retired men - although I now hear women can attend one day a week!).
I realize not everyone will have access to this sort of equipment but thought you may find it interesting.