Hello Simon,
Bolt it down for preference.
I have the same model drill, but the # 34 Jacobs chuck fits directly onto a Jacobs taper [# 6 in my case] on the end of the spindle. There is a screwed collar with a tommy bar hole (not terribly effective, I use pipe grips now) behind the chuck to be able to push the chuck off the taper.
You have a Morse taper end to your spindle which I think is a better fitting but the daylight clearance below will be reduced correspondingly. I am confused over your tool tray that you refer to, where is that situated as it's not obvious in your picture. Your table is a little different to mine in that you have side bolting slots below the table surface, mine just has a plain flat cast top.
I've had excellent service from it since buying it, badly needing new spindle bearings, in 1962 for £25 . I have added an intermediate pulley cluster between motor and spindle to get the lower speeds down for drilling the larger holes, that facility is used less now that it has an old 3 speed washing machine induction motor fitted instead of the 1/2 HP single speed 1425 rpm version. I can just switch between the motor windings which is a lot more convenient
My server makes it impossible now to post pictures here, I can't even put them in albums; some odd incompatibility problem which hides the appropriate upload button. I you want to see some PM me with your email address
Regards
Brian