Best Integrated Amp for KEF Reference 1s Under $5K New or Used

Hi all

New to the forums here. I recently acquired a set of KEF Reference 1s and am running them with a Primaluna Dialog Premium HP Integrated Amp with KT120s installed. Sound is very good but these speakers are apparently quite power hungry so I would like to at least do an in-home trial of another integrated with more power, to see if I am missing out on anything.

So two questions really:

1. Do you think I would benefit from an amp with more power and/or solid-state technology?

2. What integrated amp under $5K new or used would you recommend?

Some more relevant points:

• I am only considering integrated amps due to space constraints
• I am absolutely open to buying lightly used equipment
• I only listen to vinyl and already have a very good Herron Audio standalone phono stage
• I also listen on headphones so need a very good headphone port
• I don't need a built in DAC, bluetooth, tone controls, rumble filter or any other bells and whistles
  

So in summary all I really need is a single line-in connection, built-in headphone amp and volume control.

Thanks in advance.