The distinction between a "Schottky Diode" and a "Power Schottky Diode" is notional, essentially marketing terminology.
You would choose your diode depending on the maximum current expected to flow through it in forward bias operation. So just buy whatever can handle your worst-case current and is rated for the desired junction voltage.
Typically, manufacturers indicate high current (1 Amperes and up) Shottky diodes as power Schottky, though IIRC even some 100 mA rated ones have a "Power Schottky" mentioned in the datasheet.
The key in the advice in the data-sheet are the words "at least".
You will have to keep an eye on thermal management if your space is very limited. But other than that, the 15.4V of the rule of thumb is the minimum advised voltage, where 20V, 25V, even 500V would be fine.
Another rule of thumb is, that a very low Vf (forward voltage) is easier to find at the same forward current with a lower reverse breakdown voltage. So you'd be easier off finding a suitable device with Vbr = 30V than at Vbr = 300V.
I'd say a diode with Vf =< 0.4V at 5A should be possible to find at Vbr = 25V, you may have to look at diodes that can handle up to 15A or 20A, though. (Again, 5A is the minimum specified, higher never hurts).
Diodes are complex things, so I have taken the liberty to suggest one by having Farnell sort by price within given specifications (as your example was through hole, I'm skipping SMDs):
http://nl.farnell.com/taiwan-semiconductor/sr1203/diode-rectif-30v-12a-do-201ad/dp/1863145
Has a nice data-sheet showing in a graph that it approximately has a Vf of 0.42V at If of 5A. Still, that's quite a lot of power to dissipate, if the 5A is a regular thing, as stated, you should find a way to cool it. One option is lots of copper space connected to the pins.
As an example of my point, from the same series, the device that handles 15A in stead of 12A, the Vf goes from 0.42V to 0.4V at 5A (see data-sheet, graph on page 2, left side, second from the top):
http://nl.farnell.com/taiwan-semiconductor/sr1503/diode-rectif-30v-15a-r-6/dp/1863148
And if you could fit one in, this TO220 type makes cooling a "breeze", by just adding a heat-sink, if that's necessary, as it again has a slightly lower Vf. I have to estimate it to be about 0.30 to 0.33V at 5A, because the data-sheet has no fancy graphs:
http://nl.farnell.com/ixys-semiconductor/dssk38-0025b/diode-schottky-2x20a-25v/dp/1080066
I hope this clarifies some things for you.
My exercise of increasing cost for lower Vf/higher Current can be done with many different supplier websites, such as Mouser, DigiKey (though I find their site more annoying), or as I did, Farnell. Keep in mind, you want low Vf and the Vf rated on the cover sheet / supplier page is almost always at its rated current, where a lower current means a lower Vf. So a device of Vf = 0.5V at 25A rated will become slightly less hot at 5A than one rated for Vf = 0.5V at If = 5A.
Best Answer
Maybe you should consider the standard MOSFET circuit (but modified) that acts as a very low volt drop diode i.e. it protects a circuit from reverse polarity but turns the MOSFET on so that forward volt drop is barely a few milli volts. The basic circuit is this: -
+Vin is where you would connect the solar panel and +Vout is the battery connection. If you add a bipolar transistor and base resistor you get this: -
From a quick simulation, the BJT turns off the MOSFET when the battery voltage exceeds the SP voltage by about 730 mV (R3 is 10k not 100k). Between the voltages being equal and the battery being 730 mV higher there will be some hundreds of mA flowing back to the panel. However, if you are trying to protect the panels from the wrong battery being put in place (i.e. 24V instead of 12V) then it should do the trick.
It's just an idea and not proven other than by a quick sim. Caveat emptor!!