Good to hear that you like the LAA+.
I had a quick listen to your Kiwi SDR and your antenna is working well.
I'm not in the workshop so I don't have detailed figures to hand but I think that you will find it better to use the bias-tee and 12 V poser supply for use with the Kiwi SDR receiver.
The head unit has higher gain and dynamic range working at 12 V but as you say the bias-tee is not amplified.. You should be able to use it with your splitter without the extra attenuation.
The overall noise floor will reduce but you will have extra headroom for very strong signals.
BTW a Minicircuits four way splitter typically has 7 dB attenuation.