I do not understand your apprehension for using a standard PCB design program.
I also do not understand your wish for schematic symbols fitting your Vero strip board.
Do you want to print your schematic, then glue it on the strip board while soldering parts to your PCB?
I also use "Vero" board, but I find the strip board abhorrent. Cutting open the strips is a nuisance, and it is also a "reverse" operation. you have to remove connections that are already there, and if you forget one, it becomes a mess.
I only use the version with one hole per island myself, and I make a part of the connections by bending the existing wires of (wired) resistors and transistors (TO92, etc) and the other connections I make with enameled wire, which you can solder directly with a hot iron. I use 0.2mm enameled wire for all connections below 300mA, and thicker wire for both power and all higher current connections.
There is specialized software for this (See Abacom / Lochmaster) but it does not run on Linux, and as far as I know it is only "drawing the PCB" only. There is no connection with a schematic.
It would have helped if you posted a few screenshots of what you do with QCad, but whether you use a mechanical CAD program or PCB design software, there is always some mismatch. I have gone the other way, and I use KiCad for all my own designs. And also use it for my one-off matrix board designs. I first draw the schematic in the normal way, then put all the footprints on the PCB, and for a one-off project on Vero board, I use the PCB editor in such a way that the result fits on vero board. Mostly it's setting the PCB editor to a 2.54mm grid for all THT parts. If you want to use strip board, then you can easily confine yourself to only drawing horizontal tracks on one of the layers. You can even print out that layer, glue it to the PCB with water soluble glue and use it as a template for cutting the tracks. You can use the other copper layer for drawing wire bridges (you can make them all vertical if you wish).
If you want to use PCB's like the stuff with 3 holes per island, or the "Elex PCB" (see below), then you can also load them as a background image in KiCad, or you can make a template that has the same track layout in a real copper layer, and then just put your footprints on top of it. (Track names change automatically in Kicad when you put a footpint on top of it).
And you can take this concept as far as you like. For example:
1. Print the Silkscreen layer.
2. Put it on the PCB.
3. Punch holes though it with a needle.
4. Mount your parts though the holes.
5. Either leave the paper permanently (it may start conducting if it gets dirty / wet) or tear it to pieces and remove it.
For me, the advantages of using KiCad (or other dedicated PCB design program) are:
1. No extra constraints while drawing the schematic. Use labels, schematic symbols that reflect function instead of pinout etc.
2. Quite big libraries (around 20.000 parts in KiCad).
3. PCB footprints have real dimensions. (TO220 etc,) But use a few modified footprint for things like TO-92 so their pin spacing is 2.54mm.
4. ERC and DRC for error checking. (This is a big one!)
5. Because I use both the schematic and the PCB part. I can optimize the PCB part for layout on my matrix board.
6. I already know KiCad, no new software to learn.
7. Schematic parts are re-usable. (Just copy from a "standalone" instance into a project).
8. Schematic is re-usable if you decide later you do want to make a PCB of it.