I assume by "Sorry to bug you again about this" that you were already given help with "X", so instead of an apology, perhaps a thank you would work better:
Thank you for your help with X, but we are still having problems with it and...
This is most likely how I would write it, an apology seems to be an admission that you feel "bad" for asking and can sound "whiny", while a thank you gives the idea that you feel "good" about their previous help and appreciate it.
If you are paying for this service or for support (which you may not be), I wouldn't worry about apologizing for requesting it, especially if your previous request was not attended to.
I would like to use examples of the two sentences above in an email directed to an organization, but I would like to avoid using "you" or "bug", if possible.
I don't think it's quite necessary to avoid these two words, but there are a number of options if this is your goal. For example:
- Sorry to be a bother...
- Sorry to burden your staff with this... (still uses a form of "you")
- I/We apologize for the repeated request...
Personally, in any case I would drop the apology or thank you, in fact all extraneous parts of the email altogether. Busy people like to get things done quickly, and if their staff has a lot of work they'll appreciate a to-the-point email. However, it depends, and I recognize that this viewpoint avoids the literal question of what to replace those two words with.
You may add interaction with negation to your list of restrictions.
The second verb is in the plain form, as is evident when we test with be: We always try and be/*are helpful.
Negation
One property to add to your list of restrictions is interaction with negation.
There is an extensive discussion of try and in Webster's Dictionary of English Usage, where, in addition to some of the restrictions you have already listed, they also note the following:
A negative may precede try and, but if a negative follows try, to is used:
... when you are on your moorings, don't try and get into her—Peter Heaton, Cruising, 1952
Not to try and keep either a diary or careful income tax records —And More by Andy Rooney, 1982
Try not to take her out shopping —nurse quoted in McCall's, March 1971
The second verb is in the plain form
Here is the relevant discussion from CGEL (p. 1302), which includes some other interesting observations.
(b) Try/be sure and V
[32] PLAIN FORM + PLAIN FORM PLAIN PRESENT + PLAIN FORM
i a. Try and not be so touchy. b. We always try and do our best. [try]
ii a. Be sure and lock up. b. [not possible] [be sure]
This is very different, semantically and syntactically, from the ordinary use of and. Note first that, unlike the clausal coordination We always try and we do our best, [ib] does not entail that we do our best. Secondly, this idiomatic construction is syntactically restricted so that and must immediately follow the lexical base try; this means that there can be no inflectional suffix and no adjuncts: She always tries and does her best and We try hard and do our best can only be ordinary coordinations. There are two forms that consist simply of the lexical base: the plain form, as in [ia], and the plain present tense, as in [ib]. But the verb following and is always a plain form, as is evident when we test with be: We always try and be/*are helpful. In spite of the and, therefore, this construction is subordinative, not coordinative: and introduces a non-finite complement of try. And can be replaced by the infinitival marker to, and being slightly more informal than to. Be sure works in the same way as try, except that the lexical base of be is only the plain form, so this time there is no plain present tense matching [ib]: We are always sure and do our best is not possible as an example of this construction (and unlikely as an ordinary coordination). Because the construction is subordinative, the across the board restriction does not apply: This is something [that you must try/be sure and remedy].
Other constructions in which and replaces a possible to
Relevant to your discussion with John Lawler, Webster's Dictionary of English Usage also says that
Quite a few commentators lump try and with other constructions in which and replaces a possible to. Go and is the oldest of these, dating back to the 13th century. It has always been respectable in speech and casual writing... Unlike try and, go and can be inflected, as in these constructions: ... and he went and sat on a stone —Kay Cicellis, Encounter, March 1955... Come and is also old, and equally respectable... Be sure and is also frequently encountered.
There are a few other verbs that turn up with and where to could have been used:
He didn't have to stop and think about his answer—Elmer Davis, But We Were Born Free, 1954
And you can tell your daddy that someday I'll be President of this country. You watch and see —Lyndon B. Johnson, quoted in Sam Houston Johnson,
My Brother Lyndon, 1970
If you want to write, start and write down your thoughts —Leacock 1943
They also mention take and (Homer was courting a second time to get him a good wife and a home-keeper for his children, when he took and fell off the church-house roof —Maristan Chapman, The Happy Mountain, 1928)
The Columbia Guide to Standard American English also mentions up and (He up(ped) and punched me in the nose).
Best Answer
To my ears "for more information..." sounds more natural. An Ngram with both phrases shows that "for more information" is far more common. I would probably use "for more information," even though neither are wrong per se.
To answer the other question, there is nothing ungrammatical about starting a sentence with an infinitive, as discussed in this post: Can I start a sentence with To + verb?.