Reference Data but Skip Blank Fields?

Hi there! I'm new, but I'll try my best at explaining what I'm looking for.

I use a spreadsheet to populate 40+ 25-page contracts via Word mail merge. The contracts require a table with a list of items and their cost. However, each contract has different combinations of a set of 12 or so items with different costs for each item.

I have the Excel document set up with two sheets; one (Sheet1) is the more user-friendly version in which the basic information can be entered, and the other sheet (Sheet2) references the data from Sheet1 but with all the necessary formatting for the merge. I currently have all of the cost data in Sheet 1 by columns, essentially something like this:

Item1 Item2 Item3
ContractA ACost1 ACost3
ContractB BCost1 BCost2
ContractC CCost2 CCost3
ContractD DCost1 DCost3

I would like to be able to reference this data in Sheet2, skipping over any blank fields like so:

ContractA Item1 ACost1 Item3 ACost3
ContractB Item1 BCost1 Item2 BCost2
ContractC Item2 CCost2 Item3 CCost3
ContractD Item1 DCost1 Item3 DCost3


Does anyone know how I can do this?

EDIT: An example workbook is attached.

This proposed solution employs two formulas and a conditional formatting rule.
The first formula* which populates the columns that display the 'Items' is:

Formula:

=IFERROR(INDEX(Sheet1!$B$1:$E$1,SMALL(IF(Sheet1!$B2:$E2<>"",COLUMN($B:$E)-1),VALUE(RIGHT(B$1,1)))),"")

The second formula which populates the columns that display the cost is:

Formula:

=SUMPRODUCT((Sheet1!$A$2:$A$5=$A2)*(Sheet1!$B$1:$E$1=B2)*(Sheet1!$B$2:$E$5))

The conditional formatting rule is applied to the cost columns and hides zero values.
*The first formula must be array entered meaning that you must simultaneously press the Ctrl, Shift and Enter keys to activate.
Let us know if you have any questions.