Jp . . . Tls has given good advice above. It did not occur to me that the Integra would not output digital sources to the tape outs. I think the direction you're going now can yield very good music results. The only thing I would add is this - Clearly finding an integrated with HT passthru is the best/most ideal solution, however it's not essential. You can achieve the same results by using any integrated and taking the "main outs" from the Integra into any line level input on the integrated. If set up this way it's necessary to set up your HT outputs with the volume level on the integrated set at a level you can repeat. For example, set the volume on the integrated at 12:00 when caligrating your HT settings. Then every time you use your HT, you set the integrated at 12:00, then your Integra volume level controls loudness adjustments as you desire.
One other option for you that can yield even better music performance and flexibility is to get separate preamp and power amp rather than an integrated. Many preamps have HT passthru. The downside of this option is it's likely to cost more, and it takes up more space.
One other option for you that can yield even better music performance and flexibility is to get separate preamp and power amp rather than an integrated. Many preamps have HT passthru. The downside of this option is it's likely to cost more, and it takes up more space.