Affordable integrated amps with HT bypass?

I own a Rotel RA-1062 integrated amp, a Rotel RCD-1072 CD player and 3 pairs of B&W DM 602 S3 speakers, NONE OF WHICH HAVE EVER been out of the box since purchased. (LONG story)

I LIKE the way this combination sounded when I demo'd / auditioned.

I'm finally ready to set something up in my living room.

The key is that I want one system setup for music and movies, with music the priority.

The Rotel amplifier I own is supposed to be very good at the price point but does not have HT bypass.

The newest integrated from Rotel is also supposed to sound very good but it also did not come with HT bypass.

I want to have both music and movies but I don't want to go with a one box solution because I understand AV receivers don't sound so great with music when compared to even a budget high end integrated amp.

Plus there is the issue of trying to cram too much into an AV receiver, lowering the quality of everything and the likelihood of something breaking.

Should I start over, looking for an integrated amp, that sounds good paired with my speakers and has the HT bypass feature?

Or should I keep what I have and switch speaker wires back and forth between the integrated amp that I own and like, and whatever AV receiver I end up getting, every time I want to switch between listening to music and watching a movie?

Thanks in advance for any and all advice that comes my way.
Some help please!
Believe the Marantz PM8004 has HT bypass ability. For more funds the new line of McIntosh amps do have them.
You can mimic HT bypass by simply plugging the pre-amp outs of the receiver into an analog input on the Rotel integrated. Set the volume control to the appropriate level so its output is balanced with the center and surrounds using a standard setup feature on the receiver or with a test tone and a sound level meter. When you want to listen to movies, select the input on the Rotel and set the volume control accordingly. You can mark the volume level by putting a little dot or line on the pre-amp with a Sharpie or similar. That allows you to set a reproducible volume. HT bypass would bypass the pre-amp in the Rotel, but for what you are doing having the pre-amp section of the Rotel integrated in the path is not really an issue.
I understand AV receivers don't sound so great with music when compared to even a budget high end integrated amp.
There are probably instances where this is true and instances where it's not.

My advice is to replace the integrated amp with a decent AV pre/pro and separate amp. You won't compromise either system this way and possibly improve the music system. An AV pre/pro provides features for getting good sound in a room that just about every integrated amp lacks. E.g., level matching, distance delays, bass management and room mode correction. Tis a no-brainer to me.
I am a big fan of units with a HT Bypass feature, whether they are integrated amps or pre-amps. It truly allows the best of worlds, HT and high quality 2 channel stereo in one system and with the push of a button.

You do not mention budget but do seem to be quite satisfied with your current Rotel. It just doesn't have the much desired HT bypass function. I appears your Rotels specs are 60 wpc and listed under $1000. If this is the power and budget you currently wish to be at, Glenfihi already recommended a good one - the Marantz PM8004. Outstanding integrated for the money and built at Marantz' reference factory in Japan. 70 wpc and lists at $1000. This would be my first recommendation too.

Then, I would also look at the Creek Evolution 2, 80 wpc and $1100 list and the Music Hall A70.2 at 125 wpc and $1500 list. All have HT Bypass. Check Audio Advisor and Music Direct for demo pricing a lot lower than the list prices I provided. Good luck.
Paraneer, I've read great things about the Naim Nait 5i, and other amps by Musical Fidelity and Cyrus in the $1500 range. I think a few come with HT bypass - I know the Naim does. What do you know about those. I'd replace the Rotel if I'm definitely upgrading...especially since it has never once been out of it's box and I probably could get a few bucks more for it than if it were used.
Not familiar with Naim other than their cult following. I am sure you'll get plenty of opinions on this amp.

I am familiar with Musical Fidelity and their M3i at 76 wpc and $1500 list is a very good unit too. Yes, it has HT bypass. Don't know how I forgot about this one when posting my reply last night. If your budget goes up to around $1500, please put this down as a contender.

You now have 4 solid choices that would all do a fine job - Marantz, Creek, Music Hall and Musical Fidelity. I would start reading online reviews and if you have access to listen, start auditioning them. Believe it not, if it was me, I would choose the Marantz out of this group that coincidently is also the lowest in price. That's how much I think of it. Good luck
I am one of the Naim groupies. I use a Nait 5-i2 with Totem Sttaf speakers in a secondary system and really like the sound. I think it is especially good at low levels, which is not true of all systems. I have never heard it with B&W speakers. If you liked the sound of the Rotel with the B&W, why not give that a try as I described. I guess it depends on how much you are willing to spend for the convenience of not having to set the volume control for movies. That said, I am generally not a Rotel fan. I find that they tend to being harsh, which is not what the B&W really need, which is surprising since Rotel and B&W are from the same group.
What Dtc said about the Rotel and B&W combo was my direct experience. I would lose the Rotel. I would definitely check out the Nait. I found the Marantz gear that I listened to lost a little of the top end. As you age that's not good. It might just be my speakers.