TPS43061 simulation problems
Unfortunately, models made by TI are known to be heavily behavioural in nature, with plenty of discontinuities which cause convergence issues. This is no exception. The model was made for their WEBENCH, PSpice, or maybe TINA, so if it should run somewhere, it's there. It's not about a lack of compatibility, but about a difference in &quot;thinking&quot;.
You could try to soften up the overall stiffness by adding Rser to the output capacitor (BTW, 4 are useless, just make one), maybe adding Rser=10m Cpar=100u to the input source, there's not much to do if you want to use these models in particular. I couldn't make it run, but then I just got your models as they are, not from TI, so I don't know what changes you made. Though I'm sure it would have been the same hiccups.
That &quot;working circuit&quot; is from the application note (or close), which doesn't mean that it has to run everywhere. It may even fail in PSpice (I don't know, I don't have it). It's just a test schematic to be able to run it on the breadboard, not simulator.
But, you should know that models hardly ever match the devices in real life. I don't expect this one to be any different. This is particularly since right in the beginning of the subcircuit there is this note:

This model is subject to change without notice. Texas Instruments
Incorporated is not responsible for updating this model.

I don't know about you, but when someone says &quot;here's a model, don't bother me anymore, unless I bother myself&quot; that doesn't exactly inspire confidence in the model.
However, to solve your problem, there may be two ways, provided, again, that you're not fixed in this choice, and you need to work with LTspice:

Build your own model based on the datasheet. It doesn't look very different than many others, and if you use the A devices, you should come up with a model that seriously outperforms this one. I do not work for ADI, I am not making a selling point. I have worked with LTspice for many years and I can say quite sure of myself that it excells in switching aplications; this would be no problem.
If building a model is not your choice (for whatever reasons), you could use an equivalent one from LTspice's database, there are synchronous boost converters in there.

If your intent is to actually see how they perform before buying them, use the tools they used, but a simulator is not a breadboard. Whatever results you'll see, take them with an appropriately sized grain of salt.