As it is now, the solutions to these problems have varying levels of self reliance. At the bottom, most simple, with highest level of self reliance
- Own, borrow or rent a truck, pack your own things, drive your own things to your destination, return truck if not yours. Requires packing loading and driving everything yourself. Price can vary but usually cheaper than movers.
Next you've got:
- Random personal ad people with trucks. Not usually professional companies, varying levels of quality and reliability from, will probably smash and lose your shit to basically a professional. Vehicles come varying sizes, may not be suitable for large or high end moves. Price varies, quality tends to correspond with price.
- Professional movers, varying levels of quality from will probably not break your stuff to will dust off and spit shine everything you own. Service can vary from simple loading transport and unloading to complete packing, loading, transport, unloading and unpacking. Cost can get high.
- Container options. These have much of the same upsides and downsides as a truck rental, with the fun of dealing with shipping.
All of these suffer from problems with shortage of booking around common moving days, a problem that has more to do with the way moves tend to be either the end or the the middle of the month.
Anything that involves other people handling your property will have a risk of poor reliability. Movers are one of those professions, similar to landscaping and other jobs that are physically demanding, but not that difficult, so tends to be a lower paid job companies fill with unskilled and temporary labourers, the reliability of whom can be questionable.
I've probably missed some things, but after moving only a few months ago, this is kind of the summary of what I found available. I just can't really think of anything that could really do it any better under those constraints.
It doesn't work for furniture, but it can go a long way.
If you're renting you really shouldn't be spending on furniture anyway, just get rid of it.
It's getting someone else to show up and stick all your crap in containers to your satisfaction and then the reverse at the destination that's the problem.