A bit of planning advice needed please

Morning all 

I'm after a bit of advice.

I have grown some asparagus (Mary Washington variety) from seed. I started them off on the 26th of May, and plan on planting them in their final position next Spring.

After some careful thought, I have decided to prepare a bed for them in a mostly sunny position, next to my Strawberry bed (the blue beaker marks the end of it). At the moment, there are Capsicums planted in part of the asparagus bed, and they are producing loads of lovely Peppers, so I don't want to move them yet.

So..... if you wouldn't mind looking at the following picture



Hopefully you can see the area I mean. It is on the right hand side of the Strawberry bed, which is in front of the Sunflowers. I will be removing the Day Lilly bulbs in the Autumn, when the plant dies down (seems a shame to do it before).

So I will have an area of around 10ft x 8ft for the asparagus bed. I am hoping that the asparagus bed will be aligned with the courgette bed on the left of the picture.

Can I lay some weed suppression membrane down on the grass to kill it? The problem is, I am severely asthmatic, so digging it all out is completely beyond me  I was hoping that the area could be cleared by the Autumn, and then a good layer of well-rotted horse manure and compost over the top, so the winter frosts and worms could sort the bed out over the winter.

How many asparagus plants would be suitable in that area? And would my plan work?

Thanks for reading