MMICs are super easy to use at 162MHz, they're designeg to have 50ohm in &out, they just need a little power. Deadbug on a tiny bit of PCB.
the channel spacing for AIS is 25KHz and so the filter could be set a little big bigger 30-40KHz, not to much or more noise will get in , but a little wider to allow for any transmitters which either be drifting or have the modulation set a little too high. As you noticed too narrow doesn't work too well.
double the range is aout a 6db better sensitivity, so a MMIC at the antenna end or FET amp would easily get this result. The MMIC have the advantage of being very easy to work with. Even if the was a bit of filtering before the amp it should still get about an extra 10db improvement.
The Si4362 is only a receiver. For a transponder, you will have to look into the Si446x family.
However note, that GMSK encoding is only supported indirectly, which is fine for receivers but might not be up to spec for transponders. See this discussion: http://www.eevblog.com/forum/beginners/need-some-help-with-si4362-%28gfsk-vs-gmsk%29/
As for alternative sources for the IC, it looks like Farnell/Element14 has some in stock:
I currently use two kind of crystals, the larger footprint (5x3.2mm) is for this one:
I also use this smaller crystal (3.2x2.5mm) which is a bit out of spec as per Silabs application note (to large load capacitance), but works just fine for me: