Travel after ILR PEO appointment for work

Hello there,
I know several questions around this has been asked around here but i wanted to be absolutely clear given my scenario.

Basically, my husband and i are applying for ILR together on 6th Oct at the PEO office. The same evening / next morning i am due to fly to the US got a global conference with my office colleagues for 4 days. Now, i know that we are not meant to plan any travel without receiving the BRP (which is meant to come in within the following 10 days?) however i am a Singapore citizen meaning i dont actually need a visa to enter the UK for up to 6 months (but can't work and stuff..) The only point where i can see myself having problems is at the UK immigration at point of return when i say i have ILR but no substantial proof for this.

The global conference is something i really do not want to miss as much as the ILR application means to us - Will my work trip be considered an 'urgent travel' reason?

Has anyone got any ideas on how i can work around this?
Really appreciate your help!

Cheers,
Mal

have u thought about extending your same day appointment till you come back.
Since the fees are now same weather or not u apply with your partner, i would say if you still have a visa, why not apply once u are back.