The fresh press will last you until you take the drycleaner's plastic off the suit hanger. An occational iron is helpful to thwart the big creases, but don't expect to look non-wrinkly for longer than a few nanoseconds.
LOL. I know. I have my share of linen. Yours look pretty good as it is. Anyway, I'm sure my naturally wrinkly linen will look 10,000 better than the never been dry cleaned suits of many fellow colleagues. BTW, I just brought back my cream linen coat from the cleaners and they flat pressed the lapels.
You always have a very personal cut to your jackets. It's not entirely to my tastes (the fronts always seem a little abbreviated to my eyes), but you wear it well. Dare to unbutton a second shirt button!