No headphone output....options???

Look for a headphone amp that has a pass through like a Channel Islands VHP1 headphone amp. You can put it between your integrated and source and listen either through your headphones or through your speakers without having to disconnect anything. I'm sure that there are other headphone amps with this feature, I mention the Channel Islands one because I'm using one with my Sennheiser 580s, a great combination. Good luck!

Is there a tape out? That will work too.

Yes, if there is a fixed line out on your Sophia (tape out), then you could connect a dedicated headphone amp to it. May not be the solution you want to hear, as your headphone listenting will not be benefiting from the glorious tubes.... but if this is a concern, there are various tube headphone amps out there for reasonable money, such as from Antique Sound Labs and Bottlehead.
I agree, puting a device in the signal path to your speakers is probably not a good idea, and a dedicated headphone amp is, IMHO, the best way to go for better sound.

dedicated headphone amp is a must for good sound. Use the tape out.

The channel islands box will work fine. You end up having an EL34 based headphone amp. If you want to play with one, I have the same thing by another company that I'd sell wayyyyy cheaper than $150. They work great. Has volume and speaker on/off. You just need a short pair of interconnects. I can throw in a pair of those too?
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Headroom makes excellent headphone amplifier products as does Musical Fidelity. Less expensive units that are usable can be had from Rega and Creek and quite a few others (Consonance, ASL). You can buy dirt cheap of spend thousands on high end headphone amps.