Regarding the rejuvination of your Iceberg, while it is a very unforgiving rose, I wouldn't cut it right back in the first instance. Perhaps remove half of the old canes this winter, and trim back the remaining canes to plump buds on the younger green wood. When finished I can imagine the grey older wood with perhaps green spikes as laterals, each with no more than three leaf axils. This will force Iceberg to regenerate (and it will). Tell me what you've got this time next year, and we'll plan the next step. The following will help.

Below is an extract of July Culture Notes.

If you followed my suggestions on Summer Trimming (February, see below), there will not be as much work involved in pruning the plants. We took the opportunity to remove unproductive wood at that time and less work is required now. Failing that, approach pruning your modern roses first of all by distinguishing old from new wood, and work to retain only young wood on the plant. Any wood growing into and across the centre of the plant is to be removed whether old or young. Aim to give the plant a vigorous future by now removing oldest canes at the base of the plant, hopefully leaving 4 or 5 young canes for the coming season. These canes will be trimmed from the top down just above a plump bud in the leaf axil.
Do not prune modern roses by cutting rose canes crewcut style. This perpetuates the continuing existence of non-productive old wood, and considerably retards development of laterals on new wood, by effectively cutting to immature buds down the canes. Our climate is kinder than English conditions. We do not need to prune hard as is necessary there. We have inherited pruning methods from English books, but they do not apply in more temperate zones. There is no mystery to rose pruning. The object is to remove canes to encourage the plant to produce new canes. Cut out the old to create the new.

FEBRUARY extract: For April blooms, about 8 weeks before the required date, trim the plants by about one third to a plump bud. Cluster-flowered roses should be cut back to a bud beneath the cluster. (Ignore new water-shoots). Don't be concerned that you are cutting away new young growth. The blooms from this would be poor quality in March anyway. Also be sure to remove any old wood not capable of producing vigorous new growth. This will reduce the task at Winter pruning time.

If after considering these points nothing seems to fit the bill you could dig the plant up (you won't be missing out on much by setting it back a little) and examine the root system and surrounding soil for any possible clues.You might be suprised! For various reasons, relatively small patches of soil can sometimes become water repellant and will remain dry even when irrigated. If still nothing is evident, either just reposition the rose or replace some of the soil and replant it in the origional spot.

p.s sorry about book length answer but it's raining here and I'm stuck in house.
MrThrip