As @mguima and @spuck said, use PCB software to do your layouts. They will help you a lot to figure things out.
Also, don't be afraid to bridge your perfboard contacts to make tracings. This might be a pain for longer stretches, so you can still use a wire, but just fine for shorter runs and helps avoid weaving wires over your components or the pads you need to get to for your crucial/longer wiring. (I'm not assuming that you already do it, but I hope whoever taught you how to do electronics also taught you this "trick".)
If you have PCB software for layouts, you might be able to take the file to your local maker space to make a legit custom board. (If you don't know where the nearest maker space is, there are online maps to research them.) Some of them have the capability to build PCBs using CNC machines, laser cutters, and other techniques to even make them near professional quality. Quite often, you'll find other hobby level or, possibly, professional level electronics people that can help you even further.
As far as the actual professional services go, several of them can take a file online, then simply ship you the board. Some can even pre-populate the board for you. I was going to suggest Seeed Studio, but it looks like their min quantity for most PCB orders is 5.
You say making your own board is out of the question, but CNC machines that have accuracy good enough to make PCBs can be as small as about 12" cubed. They can cut the traces as well as the holes, then you don't even need the smelly acids. I've seen them on Amazon and eBay for less than $500. If you don't care too much about tiny traces, even a less than $300 CNC machine will work. Noise might be a factor, though, since they can be about as noisy as a drill, Dremel, or other small rotary tool. Some of them even use a Dremel as the cutting head.
Depending on the software that comes with the CNC machine. you might be able to use your layout file directly in the CNC machine. Depending on your layout software, you should still be able to at least export the file into something the CNC machine can use.